EduSahara™ Assignment
Name : Arithmetic Progression
Chapter : Progressions
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The first term of the A.P.
6
,
8
,
10
,
12
,
14
,
. . .
=
(i)
12
(ii)
10
(iii)
14
(iv)
6
(v)
8
Question
2
2.
The first term of the A.P.
2
3
,
13
15
,
16
15
,
19
15
,
22
15
,
. . .
=
(i)
2
3
(ii)
19
15
(iii)
16
15
(iv)
13
15
(v)
22
15
Question
3
3.
The common difference of the A.P.
7
,
13
,
19
,
. . .
=
(i)
3
(ii)
6
(iii)
8
(iv)
5
(v)
7
Question
4
4.
The common difference of the A.P.
3
5
,
32
45
,
37
45
,
. . .
=
(i)
1
9
(ii)
(
-1
9
)
(iii)
1
3
(iv)
1
7
(v)
1
11
Question
5
5.
Find
t
18
of the A.P.
5
,
9
,
13
,
. . .
=
(i)
74
(ii)
73
(iii)
71
(iv)
72
(v)
76
Question
6
6.
Find
t
11
of the A.P.
7
9
,
23
18
,
16
9
,
. . .
=
(i)
52
7
(ii)
52
11
(iii)
6
(iv)
52
9
(v)
50
9
Question
7
7.
Find
S
18
of the A.P.
9
,
10
,
11
,
. . .
=
(i)
316
(ii)
318
(iii)
312
(iv)
315
(v)
314
Question
8
8.
Find
S
5
of the A.P.
9
2
,
14
3
,
29
6
,
. . .
=
(i)
49
2
(ii)
145
4
(iii)
145
6
(iv)
145
8
(v)
143
6
Question
9
9.
Determine
t
12
of an A.P whose
t
16
is
129
and common difference is
8
(i)
96
(ii)
97
(iii)
100
(iv)
94
(v)
98
Question
10
10.
Determine
t
17
of an A.P whose
t
19
is
97
36
and common difference is
1
8
(i)
8
3
(ii)
22
7
(iii)
2
(iv)
20
9
(v)
22
9
Question
11
11.
The
t
13
of an A.P. is
30
and the
t
15
is
34
.
Find
t
19
.
(i)
40
(ii)
43
(iii)
41
(iv)
42
(v)
44
Question
12
12.
The
t
5
of an A.P. is
2
and the
t
10
is
17
6
.
Find
t
16
.
(i)
25
6
(ii)
23
6
(iii)
23
8
(iv)
23
4
(v)
7
2
Question
13
13.
Which term of the A.P.
2
,
6
,
10
,
. . .
is
22
?
(i)
t
9
(ii)
t
5
(iii)
t
4
(iv)
t
6
(v)
t
7
Question
14
14.
Which term of the A.P.
1
4
,
5
12
,
7
12
,
. . .
is
31
12
?
(i)
t
17
(ii)
t
15
(iii)
t
16
(iv)
t
13
(v)
t
14
Question
15
15.
The sum of first three terms of an A.P. is
30
while their product is
190
.
Find the A.P.
(i)
1
,
7
,
13
,
. . .
(ii)
1
,
10
,
19
,
. . .
(iii)
1
,
9
,
17
,
. . .
(iv)
2
,
11
,
20
,
. . .
(v)
3
,
12
,
21
,
. . .
Question
16
16.
The sum of first three terms of an A.P. is
3
while their product is
3
4
.
Find the A.P.
(i)
1
2
,
3
2
,
5
2
,
. . .
(ii)
1
4
,
3
4
,
5
4
,
. . .
(iii)
1
2
,
0
,
(
-1
2
)
,
. . .
(iv)
3
2
,
2
,
5
2
,
. . .
(v)
1
2
,
1
,
3
2
,
. . .
Question
17
17.
Insert
4
arithmetic means between
6
and
21
.
(i)
8
,
10
,
12
,
14
(ii)
10
,
14
,
18
,
22
(iii)
9
,
12
,
15
,
18
(iv)
6
,
6
,
6
,
6
(v)
11
,
16
,
21
,
26
Question
18
18.
Insert
3
arithmetic means between
8
7
and
68
35
.
(i)
61
35
,
82
35
,
103
35
(ii)
33
35
,
26
35
,
19
35
(iii)
47
35
,
54
35
,
61
35
(iv)
31
21
,
38
21
,
15
7
(v)
9
7
,
10
7
,
11
7
Question
19
19.
If a =
3
and d =
7
, find
t
10
of the A.P.
(i)
68
(ii)
65
(iii)
66
(iv)
63
(v)
67
Question
20
20.
If a =
9
7
and d =
1
3
, find
t
10
of the A.P.
(i)
10
3
(ii)
30
7
(iii)
4
(iv)
32
7
(v)
6
Question
21
21.
How many terms of the A.P.
4
,
12
,
20
,
. . .
are needed to
make the sum
400
?
(i)
10
(ii)
11
(iii)
13
(iv)
8
(v)
9
Question
22
22.
How many terms of the A.P.
3
5
,
17
20
,
11
10
,
. . .
are needed to
make the sum
273
10
?
(i)
15
(ii)
13
(iii)
12
(iv)
10
(v)
14
Question
23
23.
If a =
58
and b =
76
,
the arithmetic mean of a and b =
(i)
70
(ii)
66
(iii)
68
(iv)
67
(v)
65
Question
24
24.
If a =
155
56
and b =
171
56
,
the arithmetic mean of a and b =
(i)
163
56
(ii)
163
58
(iii)
23
8
(iv)
163
54
(v)
165
56
Question
25
25.
Find the sum of first 84 natural numbers
(i)
3571
(ii)
3568
(iii)
3570
(iv)
3569
(v)
3573
Question
26
26.
Find the next
4
terms of the following A.P.
(
−
2
a
−
5
b
)
,
(
−
8
a
)
,
(
−
14
a
+
5
b
)
,
. . .
(i)
(
−
22
a
+
5
b
)
,
(
−
28
a
+
10
b
)
,
(
−
34
a
+
15
b
)
,
(
−
40
a
+
20
b
)
(ii)
(
−
18
a
+
15
b
)
,
(
−
24
a
+
20
b
)
,
(
−
30
a
+
25
b
)
,
(
−
36
a
+
30
b
)
(iii)
(
−
20
a
+
10
b
)
,
(
−
26
a
+
15
b
)
,
(
−
32
a
+
20
b
)
,
(
−
38
a
+
25
b
)
(iv)
(
−
26
a
+
15
b
)
,
(
−
32
a
+
20
b
)
,
(
−
38
a
+
25
b
)
,
(
−
44
a
+
30
b
)
(v)
(
−
16
a
)
,
(
−
22
a
+
5
b
)
,
(
−
28
a
+
10
b
)
,
(
−
34
a
+
15
b
)
Question
27
27.
Find
t
n
of the A.P
1
,
9
,
17
,
25
,
33
,
. . .
(i)
(
10
n
−
7
)
(ii)
(
8
n
−
6
)
(iii)
(
6
n
−
7
)
(iv)
(
8
n
+
1
)
(v)
(
8
n
−
7
)
Question
28
28.
Find
t
n
of the A.P
3
5
,
11
10
,
8
5
,
21
10
,
13
5
,
. . .
(i)
(
−
3
2
n
+
1
10
)
(ii)
(
1
2
n
+
1
10
)
(iii)
(
1
2
n
+
3
5
)
(iv)
(
9
2
n
+
1
10
)
(v)
(
1
2
n
+
7
10
)
Question
29
29.
The
t
6
of an A.P is
p
and
t
7
is
q
.
Find
t
11
and
t
n
.
(i)
(
−
4
p
+
5
q
)
,
(
−
p
n
+
p
+
q
n
−
q
)
(ii)
(
−
4
p
+
5
q
)
,
(
−
p
n
+
7
p
+
q
n
−
6
q
)
(iii)
(
−
3
p
+
4
q
)
,
(
−
p
n
+
7
p
+
q
n
−
6
q
)
(iv)
(
−
5
p
+
6
q
)
,
(
−
p
n
+
6
p
+
q
n
−
5
q
)
(v)
2
p
,
(
−
p
n
+
13
p
+
q
n
−
11
q
)
Question
30
30.
Determine k so that
(
8
k
+
4
)
,
(
8
k
+
9
)
and
(
k
+
6
)
are the consecutive terms of an A.P
(i)
(
-6
7
)
(ii)
(
-6
5
)
(iii)
(
-10
7
)
(iv)
(
-10
9
)
(v)
(
-8
7
)
Question
31
31.
The product of two numbers is
468
and their arithmetic mean is
22
.
Find the two numbers.
(i)
(
21
,
26
)
(ii)
(
18
,
26
)
(iii)
(
28
,
20
)
(iv)
(
18
,
25
)
(v)
(
19
,
27
)
Question
32
32.
Find the common difference and next four terms of the
following A.P.
8
,
13
,
18
,
. . .
=
(i)
6
;
20
,
24
,
28
,
32
(ii)
5
;
23
,
28
,
33
,
38
(iii)
6
;
26
,
32
,
38
,
44
(iv)
6
;
23
,
28
,
33
,
38
Question
33
33.
Find the common difference and next four terms of the
following A.P.
1
9
,
17
72
,
13
36
,
. . .
=
(i)
1
1
8
;
35
72
,
11
18
,
53
72
,
31
36
(ii)
1
1
8
;
251
72
,
83
18
,
413
72
,
247
36
(iii)
1
8
;
35
72
,
11
18
,
53
72
,
31
36
(iv)
1
1
8
;
(
-181
72
)
,
(
-61
18
)
,
(
-307
72
)
,
(
-185
36
)
Question
34
34.
Find the sum of all natural numbers between 1 and 100 which are multiples of 5?
(i)
950
(ii)
952
(iii)
947
(iv)
949
(v)
951
Question
35
35.
Find the sum of all natural numbers between 100 and 200 which are multiples of 6?
(i)
2549
(ii)
2547
(iii)
2553
(iv)
2551
(v)
2550
Question
36
36.
Find the sum of the following A.P. series
(
2
x
+
3
y
)
,
(
3
x
−
2
y
)
,
(
4
x
−
7
y
)
. . .
to
11
terms
(i)
(
54
x
−
270
y
)
(ii)
(
77
x
−
242
y
)
(iii)
(
58
x
−
264
y
)
(iv)
(
64
x
−
190
y
)
(v)
(
66
x
−
200
y
)
Question
37
37.
Given a =
5
, d =
4
,
S
n
=
434
, find
t
n
(i)
60
(ii)
57
(iii)
56
(iv)
55
(v)
58
Question
38
38.
Given a =
3
, d =
2
,
S
n
=
48
, find n
(i)
3
(ii)
5
(iii)
6
(iv)
7
(v)
9
Question
39
39.
Given a =
6
, d =
7
, n =
17
, find
t
n
(i)
118
(ii)
115
(iii)
120
(iv)
117
(v)
119
Question
40
40.
Given a =
2
, d =
6
, n =
15
, find
S
n
(i)
663
(ii)
659
(iii)
658
(iv)
661
(v)
660
Question
41
41.
Given
t
n
=
59
, n =
14
,
S
n
=
462
, find a
(i)
6
(ii)
8
(iii)
4
(iv)
7
(v)
9
Question
42
42.
Given
t
n
=
69
, n =
13
,
S
n
=
507
, find d
(i)
3
(ii)
8
(iii)
4
(iv)
6
(v)
5
Question
43
43.
Given
t
n
=
31
, d =
3
, n =
10
, find a
(i)
7
(ii)
4
(iii)
1
(iv)
3
(v)
5
Question
44
44.
Given
t
n
=
71
, d =
5
, n =
14
, find
S
n
(i)
536
(ii)
538
(iii)
540
(iv)
541
(v)
539
Question
45
45.
Given
t
n
=
10
, a =
2
, n =
5
, find
S
n
(i)
33
(ii)
29
(iii)
28
(iv)
30
(v)
31
Question
46
46.
Given
t
n
=
61
, a =
5
, n =
8
, find d
(i)
7
(ii)
5
(iii)
9
(iv)
8
(v)
11
Question
47
47.
Find
t
n
of the A.P
4
,
11
,
18
,
. . .
(i)
(
8
n
−
3
)
(ii)
(
7
n
+
4
)
(iii)
(
6
n
−
3
)
(iv)
(
7
n
+
1
)
(v)
(
7
n
−
3
)
Question
48
48.
If
S
60
and
S
80
of an A.P. are
4020
and
6960
respectively, then
S
140
=
(i)
20580
(ii)
20582
(iii)
20578
(iv)
20581
Question
49
49.
If x
≠
y and the sequences x ,
a
1
,
a
2
, y and x ,
b
1
,
b
2
, y
each are in A.P., then
a
2
−
a
1
b
2
−
b
1
=
(i)
3
2
(ii)
(
-3
4
)
(iii)
1
(iv)
2
3
(v)
4
3
Question
50
50.
If there are n arithmetic means between a and b, the common difference d =
(i)
(
a
+
b
)
(
n
+
1
)
(ii)
(
b
−
a
)
(
n
−
1
)
(iii)
(
b
−
a
)
(
n
+
1
)
(iv)
(
a
−
b
)
(
n
+
1
)
(v)
(
n
−
1
)
(
a
+
b
)
Question
51
51.
The sum of first n natural number is
(i)
(
n
)
(
n
+
1
)
(
2
n
+
1
)
6
(ii)
(
n
−
1
)
(
n
+
1
)
2
(iii)
(
n
)
(
n
−
1
)
2
(iv)
n
2
(
n
+
1
)
2
4
(v)
(
n
)
(
n
+
1
)
2
Question
52
52.
The measures of the interior angles of a convex polygon are in A.P.
If the smallest angle is
135
and the largest angle is
165
,
then the number of sides of the polygon is
(i)
11
(ii)
12
(iii)
13
(iv)
15
(v)
9
Question
53
53.
If the
t
n
of an A.P is
(
4
n
+
8
)
, find
S
n
(i)
(
3
)
(
n
2
+
n
)
2
+
3
n
(ii)
(
2
)
(
n
2
+
n
)
2
+
2
n
(iii)
(
6
)
(
n
2
+
n
)
2
+
4
n
(iv)
(
7
)
(
n
2
+
n
)
2
+
n
(v)
(
4
)
(
n
2
+
n
)
2
+
8
n
Assignment Key
1) (iv)
2) (i)
3) (ii)
4) (i)
5) (ii)
6) (iv)
7) (iv)
8) (iii)
9) (ii)
10) (v)
11) (iv)
12) (ii)
13) (iv)
14) (ii)
15) (ii)
16) (v)
17) (iii)
18) (iii)
19) (iii)
20) (ii)
21) (i)
22) (ii)
23) (iv)
24) (i)
25) (iii)
26) (iii)
27) (v)
28) (ii)
29) (ii)
30) (v)
31) (ii)
32) (ii)
33) (iii)
34) (i)
35) (v)
36) (ii)
37) (ii)
38) (iii)
39) (i)
40) (v)
41) (iv)
42) (v)
43) (ii)
44) (v)
45) (iv)
46) (iv)
47) (v)
48) (i)
49) (iii)
50) (iii)
51) (v)
52) (ii)
53) (v)
