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.
4
,
9
,
14
,
19
,
24
,
. . .
=
(i)
24
(ii)
9
(iii)
14
(iv)
4
(v)
19
Question
2
2.
The first term of the A.P.
5
4
,
3
2
,
7
4
,
2
,
9
4
,
. . .
=
(i)
5
4
(ii)
7
4
(iii)
3
2
(iv)
9
4
(v)
2
Question
3
3.
The common difference of the A.P.
5
,
11
,
17
,
. . .
=
(i)
6
(ii)
5
(iii)
7
(iv)
4
(v)
8
Question
4
4.
The common difference of the A.P.
3
5
,
29
40
,
17
20
,
. . .
=
(i)
3
8
(ii)
1
6
(iii)
1
8
(iv)
1
10
(v)
(
-1
8
)
Question
5
5.
Find
t
13
of the A.P.
8
,
17
,
26
,
. . .
=
(i)
115
(ii)
114
(iii)
117
(iv)
119
(v)
116
Question
6
6.
Find
t
13
of the A.P.
7
2
,
4
,
9
2
,
. . .
=
(i)
19
4
(ii)
17
2
(iii)
19
2
(iv)
21
2
(v)
19
Question
7
7.
Find
S
19
of the A.P.
9
,
17
,
25
,
. . .
=
(i)
1541
(ii)
1538
(iii)
1540
(iv)
1536
(v)
1539
Question
8
8.
Find
S
18
of the A.P.
6
5
,
29
20
,
17
10
,
. . .
=
(i)
1199
20
(ii)
133
2
(iii)
239
4
(iv)
1197
22
(v)
1197
20
Question
9
9.
Determine
t
16
of an A.P whose
t
15
is
79
and common difference is
5
(i)
85
(ii)
83
(iii)
84
(iv)
82
(v)
86
Question
10
10.
Determine
t
10
of an A.P whose
t
12
is
67
18
and common difference is
1
9
(i)
7
4
(ii)
7
(iii)
7
2
(iv)
9
2
(v)
5
2
Question
11
11.
The
t
17
of an A.P. is
120
and the
t
19
is
134
.
Find
t
13
.
(i)
95
(ii)
90
(iii)
92
(iv)
93
(v)
91
Question
12
12.
The
t
5
of an A.P. is
13
9
and the
t
14
is
40
9
.
Find
t
10
.
(i)
4
(ii)
28
9
(iii)
26
9
(iv)
28
11
(v)
10
3
Question
13
13.
Which term of the A.P.
7
,
11
,
15
,
. . .
is
83
?
(i)
t
18
(ii)
t
19
(iii)
t
22
(iv)
t
21
(v)
t
20
Question
14
14.
Which term of the A.P.
5
6
,
41
42
,
47
42
,
. . .
is
149
42
?
(i)
t
20
(ii)
t
23
(iii)
t
19
(iv)
t
18
(v)
t
21
Question
15
15.
The sum of first three terms of an A.P. is
33
while their product is
1232
.
Find the A.P.
(i)
8
,
9
,
10
,
. . .
(ii)
8
,
10
,
12
,
. . .
(iii)
10
,
13
,
16
,
. . .
(iv)
9
,
12
,
15
,
. . .
(v)
8
,
11
,
14
,
. . .
Question
16
16.
The sum of first three terms of an A.P. is
31
7
while their product is
4216
1323
.
Find the A.P.
(i)
4
5
,
33
35
,
38
35
,
. . .
(ii)
4
3
,
25
21
,
22
21
,
. . .
(iii)
4
3
,
23
15
,
26
15
,
. . .
(iv)
4
3
,
31
21
,
34
21
,
. . .
(v)
2
,
15
7
,
16
7
,
. . .
Question
17
17.
Insert
1
arithmetic means between
4
and
22
.
(i)
14
(ii)
16
(iii)
12
(iv)
11
(v)
13
Question
18
18.
Insert
1
arithmetic means between
7
6
and
61
42
.
(i)
43
42
(ii)
23
18
(iii)
55
42
(iv)
67
42
(v)
41
30
Question
19
19.
If a =
8
and d =
5
, find
t
10
of the A.P.
(i)
53
(ii)
51
(iii)
52
(iv)
56
(v)
54
Question
20
20.
If a =
7
3
and d =
1
6
, find
t
2
of the A.P.
(i)
3
2
(ii)
5
2
(iii)
5
4
(iv)
7
2
(v)
5
Question
21
21.
How many terms of the A.P.
4
,
5
,
6
,
. . .
are needed to
make the sum
270
?
(i)
21
(ii)
19
(iii)
23
(iv)
18
(v)
20
Question
22
22.
How many terms of the A.P.
2
7
,
17
35
,
24
35
,
. . .
are needed to
make the sum
1387
35
?
(i)
16
(ii)
20
(iii)
22
(iv)
19
(v)
18
Question
23
23.
If a =
131
and b =
147
,
the arithmetic mean of a and b =
(i)
141
(ii)
140
(iii)
139
(iv)
138
(v)
136
Question
24
24.
If a =
31
8
and b =
33
8
,
the arithmetic mean of a and b =
(i)
1
(ii)
3
(iii)
4
(iv)
6
(v)
5
Question
25
25.
Find the sum of first 59 natural numbers
(i)
1769
(ii)
1767
(iii)
1771
(iv)
1770
(v)
1773
Question
26
26.
Find the next
4
terms of the following A.P.
(
6
a
−
8
b
)
,
(
14
a
−
6
b
)
,
(
22
a
−
4
b
)
,
. . .
(i)
38
a
,
(
46
a
+
2
b
)
,
(
54
a
+
4
b
)
,
(
62
a
+
6
b
)
(ii)
(
30
a
−
2
b
)
,
38
a
,
(
46
a
+
2
b
)
,
(
54
a
+
4
b
)
(iii)
(
24
a
+
6
b
)
,
(
32
a
+
8
b
)
,
(
40
a
+
10
b
)
,
(
48
a
+
12
b
)
(iv)
(
28
a
−
12
b
)
,
(
36
a
−
10
b
)
,
(
44
a
−
8
b
)
,
(
52
a
−
6
b
)
(v)
(
36
a
−
10
b
)
,
(
44
a
−
8
b
)
,
(
52
a
−
6
b
)
,
(
60
a
−
4
b
)
Question
27
27.
Find
t
n
of the A.P
2
,
3
,
4
,
5
,
6
,
. . .
(i)
1
(ii)
(
n
+
1
)
(iii)
(
n
+
2
)
(iv)
(
4
n
+
1
)
(v)
(
n
+
3
)
Question
28
28.
Find
t
n
of the A.P
3
8
,
35
72
,
43
72
,
17
24
,
59
72
,
. . .
(i)
(
−
35
9
n
+
19
72
)
(ii)
(
1
9
n
+
19
72
)
(iii)
(
1
9
n
+
3
8
)
(iv)
(
1
9
n
+
23
36
)
(v)
(
37
9
n
+
19
72
)
Question
29
29.
The
t
6
of an A.P is
p
and
t
7
is
q
.
Find
t
18
and
t
n
.
(i)
(
−
11
p
+
12
q
)
,
(
−
p
n
+
7
p
+
q
n
−
6
q
)
(ii)
(
−
5
p
+
7
q
)
,
(
−
p
n
+
13
p
+
q
n
−
11
q
)
(iii)
(
−
10
p
+
11
q
)
,
(
−
p
n
+
7
p
+
q
n
−
6
q
)
(iv)
(
−
12
p
+
13
q
)
,
(
−
p
n
+
6
p
+
q
n
−
5
q
)
(v)
(
−
11
p
+
12
q
)
,
(
−
p
n
+
p
+
q
n
−
q
)
Question
30
30.
Determine k so that
(
6
k
+
7
)
,
(
7
k
+
7
)
and
(
3
k
+
5
)
are the consecutive terms of an A.P
(i)
(
-2
7
)
(ii)
(
-2
3
)
(iii)
(
-2
5
)
(iv)
(
-4
5
)
(v)
0
Question
31
31.
The product of two numbers is
520
and their arithmetic mean is
23
.
Find the two numbers.
(i)
(
20
,
26
)
(ii)
(
21
,
27
)
(iii)
(
28
,
22
)
(iv)
(
22
,
26
)
(v)
(
20
,
25
)
Question
32
32.
Find the common difference and next four terms of the
following A.P.
8
,
17
,
26
,
. . .
=
(i)
10
;
32
,
40
,
48
,
56
(ii)
10
;
38
,
48
,
58
,
68
(iii)
10
;
35
,
44
,
53
,
62
(iv)
9
;
35
,
44
,
53
,
62
Question
33
33.
Find the common difference and next four terms of the
following A.P.
5
8
,
19
24
,
23
24
,
. . .
=
(i)
1
1
6
;
(
-15
8
)
,
(
-65
24
)
,
(
-85
24
)
,
(
-35
8
)
(ii)
1
1
6
;
33
8
,
127
24
,
155
24
,
61
8
(iii)
1
6
;
9
8
,
31
24
,
35
24
,
13
8
(iv)
1
1
6
;
9
8
,
31
24
,
35
24
,
13
8
Question
34
34.
Find the sum of all natural numbers between 1 and 100 which are multiples of 9?
(i)
593
(ii)
592
(iii)
595
(iv)
594
(v)
596
Question
35
35.
Find the sum of all natural numbers between 100 and 200 which are multiples of 3?
(i)
4953
(ii)
4950
(iii)
4949
(iv)
4948
(v)
4951
Question
36
36.
Find the sum of the following A.P. series
(
9
x
+
8
y
)
,
(
18
x
+
12
y
)
,
(
27
x
+
16
y
)
. . .
to
12
terms
(i)
(
603
x
+
276
y
)
(ii)
(
702
x
+
360
y
)
(iii)
(
585
x
+
260
y
)
(iv)
(
603
x
+
312
y
)
(v)
(
585
x
+
304
y
)
Question
37
37.
Given a =
5
, d =
3
,
S
n
=
220
, find
t
n
(i)
33
(ii)
36
(iii)
34
(iv)
38
(v)
35
Question
38
38.
Given a =
4
, d =
4
,
S
n
=
312
, find n
(i)
11
(ii)
9
(iii)
13
(iv)
15
(v)
12
Question
39
39.
Given a =
2
, d =
2
, n =
20
, find
t
n
(i)
39
(ii)
41
(iii)
38
(iv)
40
(v)
43
Question
40
40.
Given a =
6
, d =
3
, n =
6
, find
S
n
(i)
84
(ii)
80
(iii)
81
(iv)
79
(v)
82
Question
41
41.
Given
t
n
=
139
, n =
20
,
S
n
=
1450
, find a
(i)
5
(ii)
7
(iii)
3
(iv)
9
(v)
6
Question
42
42.
Given
t
n
=
33
, n =
5
,
S
n
=
105
, find d
(i)
8
(ii)
5
(iii)
7
(iv)
3
(v)
6
Question
43
43.
Given
t
n
=
17
, d =
3
, n =
5
, find a
(i)
5
(ii)
8
(iii)
2
(iv)
6
(v)
4
Question
44
44.
Given
t
n
=
39
, d =
6
, n =
6
, find
S
n
(i)
143
(ii)
142
(iii)
147
(iv)
144
(v)
145
Question
45
45.
Given
t
n
=
104
, a =
2
, n =
18
, find
S
n
(i)
955
(ii)
954
(iii)
952
(iv)
956
(v)
953
Question
46
46.
Given
t
n
=
65
, a =
8
, n =
20
, find d
(i)
0
(ii)
5
(iii)
2
(iv)
4
(v)
3
Question
47
47.
Find
t
n
of the A.P
4
,
10
,
16
,
. . .
(i)
(
10
n
−
2
)
(ii)
(
5
n
−
2
)
(iii)
(
6
n
+
2
)
(iv)
(
6
n
+
4
)
(v)
(
6
n
−
2
)
Question
48
48.
If
S
30
and
S
60
of an A.P. are
4185
and
16470
respectively, then
S
90
=
(i)
36855
(ii)
36856
(iii)
36857
(iv)
36852
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)
1
(iii)
(
-3
4
)
(iv)
4
3
(v)
2
3
Question
50
50.
If there are n arithmetic means between a and b, the common difference d =
(i)
(
a
−
b
)
(
n
+
1
)
(ii)
(
a
+
b
)
(
n
+
1
)
(iii)
(
n
−
1
)
(
a
+
b
)
(iv)
(
b
−
a
)
(
n
−
1
)
(v)
(
b
−
a
)
(
n
+
1
)
Question
51
51.
The sum of first n natural number is
(i)
n
2
(
n
+
1
)
2
4
(ii)
(
n
−
1
)
(
n
+
1
)
2
(iii)
(
n
)
(
n
+
1
)
(
2
n
+
1
)
6
(iv)
(
n
)
(
n
−
1
)
2
(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
83
and the largest angle is
133
,
then the number of sides of the polygon is
(i)
4
(ii)
7
(iii)
5
(iv)
2
(v)
6
Question
53
53.
If the
t
n
of an A.P is
(
n
+
8
)
, find
S
n
(i)
(
1
)
(
n
2
+
n
)
2
+
8
n
(ii)
(
6
)
(
n
2
+
n
)
2
+
7
n
(iii)
(
6
)
(
n
2
+
n
)
2
+
8
n
(iv)
(
8
)
(
n
2
+
n
)
2
+
8
n
(v)
(
7
)
(
n
2
+
n
)
2
+
4
n
Assignment Key
1) (iv)
2) (i)
3) (i)
4) (iii)
5) (v)
6) (iii)
7) (v)
8) (v)
9) (iii)
10) (iii)
11) (iii)
12) (ii)
13) (v)
14) (i)
15) (v)
16) (iv)
17) (v)
18) (iii)
19) (i)
20) (ii)
21) (v)
22) (iv)
23) (iii)
24) (iii)
25) (iv)
26) (ii)
27) (ii)
28) (ii)
29) (i)
30) (iii)
31) (i)
32) (iv)
33) (iii)
34) (iv)
35) (ii)
36) (ii)
37) (v)
38) (v)
39) (iv)
40) (iii)
41) (v)
42) (v)
43) (i)
44) (iv)
45) (ii)
46) (v)
47) (v)
48) (i)
49) (ii)
50) (v)
51) (v)
52) (iii)
53) (i)
