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.
8
,
14
,
20
,
26
,
32
,
. . .
=
(i)
14
(ii)
20
(iii)
8
(iv)
32
(v)
26
Question
2
2.
The first term of the A.P.
5
8
,
53
72
,
61
72
,
23
24
,
77
72
,
. . .
=
(i)
5
8
(ii)
53
72
(iii)
77
72
(iv)
23
24
(v)
61
72
Question
3
3.
The common difference of the A.P.
8
,
9
,
10
,
. . .
=
(i)
0
(ii)
1
(iii)
-2
(iv)
3
(v)
2
Question
4
4.
The common difference of the A.P.
5
7
,
32
35
,
39
35
,
. . .
=
(i)
(
-1
5
)
(ii)
1
5
(iii)
1
7
(iv)
3
5
(v)
1
3
Question
5
5.
Find
t
13
of the A.P.
6
,
7
,
8
,
. . .
=
(i)
18
(ii)
17
(iii)
21
(iv)
15
(v)
19
Question
6
6.
Find
t
6
of the A.P.
1
5
,
9
20
,
7
10
,
. . .
=
(i)
29
22
(ii)
27
20
(iii)
31
20
(iv)
29
18
(v)
29
20
Question
7
7.
Find
S
22
of the A.P.
5
,
14
,
23
,
. . .
=
(i)
2186
(ii)
2192
(iii)
2188
(iv)
2190
(v)
2189
Question
8
8.
Find
S
19
of the A.P.
5
8
,
43
56
,
51
56
,
. . .
=
(i)
2033
56
(ii)
2031
56
(iii)
2035
56
(iv)
2033
54
(v)
2033
58
Question
9
9.
Determine
t
7
of an A.P whose
t
19
is
42
and common difference is
2
(i)
17
(ii)
18
(iii)
20
(iv)
19
(v)
16
Question
10
10.
Determine
t
15
of an A.P whose
t
6
is
106
45
and common difference is
1
9
(i)
151
45
(ii)
149
45
(iii)
151
43
(iv)
17
5
(v)
151
47
Question
11
11.
The
t
11
of an A.P. is
56
and the
t
12
is
61
.
Find
t
13
.
(i)
66
(ii)
68
(iii)
67
(iv)
65
(v)
63
Question
12
12.
The
t
11
of an A.P. is
11
5
and the
t
16
is
16
5
.
Find
t
8
.
(i)
8
7
(ii)
2
(iii)
6
5
(iv)
8
3
(v)
8
5
Question
13
13.
Which term of the A.P.
6
,
10
,
14
,
. . .
is
58
?
(i)
t
16
(ii)
t
13
(iii)
t
11
(iv)
t
14
(v)
t
15
Question
14
14.
Which term of the A.P.
7
6
,
55
42
,
61
42
,
. . .
is
121
42
?
(i)
t
13
(ii)
t
14
(iii)
t
12
(iv)
t
11
(v)
t
16
Question
15
15.
The sum of first three terms of an A.P. is
24
while their product is
312
.
Find the A.P.
(i)
3
,
5
,
7
,
. . .
(ii)
3
,
8
,
13
,
. . .
(iii)
4
,
9
,
14
,
. . .
(iv)
5
,
10
,
15
,
. . .
(v)
3
,
7
,
11
,
. . .
Question
16
16.
The sum of first three terms of an A.P. is
14
15
while their product is
266
10125
.
Find the A.P.
(i)
3
5
,
32
45
,
37
45
,
. . .
(ii)
1
7
,
16
63
,
23
63
,
. . .
(iii)
1
5
,
12
35
,
17
35
,
. . .
(iv)
1
5
,
14
45
,
19
45
,
. . .
(v)
1
5
,
4
45
,
(
-1
45
)
,
. . .
Question
17
17.
Insert
2
arithmetic means between
4
and
19
.
(i)
12
,
20
(ii)
10
,
16
(iii)
8
,
12
(iv)
6
,
8
(v)
9
,
14
Question
18
18.
Insert
1
arithmetic means between
3
7
and
5
7
.
(i)
22
35
(ii)
6
7
(iii)
34
63
(iv)
2
7
(v)
4
7
Question
19
19.
If a =
6
and d =
1
, find
t
9
of the A.P.
(i)
17
(ii)
12
(iii)
14
(iv)
13
(v)
15
Question
20
20.
If a =
7
5
and d =
1
6
, find
t
6
of the A.P.
(i)
67
32
(ii)
23
10
(iii)
67
28
(iv)
13
6
(v)
67
30
Question
21
21.
How many terms of the A.P.
9
,
12
,
15
,
. . .
are needed to
make the sum
684
?
(i)
18
(ii)
19
(iii)
17
(iv)
20
(v)
21
Question
22
22.
How many terms of the A.P.
4
7
,
19
21
,
26
21
,
. . .
are needed to
make the sum
429
7
?
(i)
18
(ii)
19
(iii)
16
(iv)
21
(v)
17
Question
23
23.
If a =
11
and b =
13
,
the arithmetic mean of a and b =
(i)
14
(ii)
11
(iii)
10
(iv)
13
(v)
12
Question
24
24.
If a =
45
7
and b =
149
21
,
the arithmetic mean of a and b =
(i)
48
7
(ii)
142
19
(iii)
142
23
(iv)
142
21
(v)
20
3
Question
25
25.
Find the sum of first 73 natural numbers
(i)
2702
(ii)
2704
(iii)
2700
(iv)
2699
(v)
2701
Question
26
26.
Find the next
4
terms of the following A.P.
(
9
a
+
3
b
)
,
(
13
a
+
10
b
)
,
(
17
a
+
17
b
)
,
. . .
(i)
(
30
a
+
27
b
)
,
(
34
a
+
34
b
)
,
(
38
a
+
41
b
)
,
(
42
a
+
48
b
)
(ii)
(
25
a
+
31
b
)
,
(
29
a
+
38
b
)
,
(
33
a
+
45
b
)
,
(
37
a
+
52
b
)
(iii)
(
21
a
+
24
b
)
,
(
25
a
+
31
b
)
,
(
29
a
+
38
b
)
,
(
33
a
+
45
b
)
(iv)
(
12
a
+
21
b
)
,
(
16
a
+
28
b
)
,
(
20
a
+
35
b
)
,
(
24
a
+
42
b
)
(v)
(
26
a
+
20
b
)
,
(
30
a
+
27
b
)
,
(
34
a
+
34
b
)
,
(
38
a
+
41
b
)
Question
27
27.
Find
t
n
of the A.P
8
,
12
,
16
,
20
,
24
,
. . .
(i)
(
4
n
+
8
)
(ii)
(
4
n
+
4
)
(iii)
(
3
n
+
4
)
(iv)
(
4
n
+
12
)
(v)
(
5
n
+
4
)
Question
28
28.
Find
t
n
of the A.P
6
5
,
41
30
,
23
15
,
17
10
,
28
15
,
. . .
(i)
(
−
17
6
n
+
31
30
)
(ii)
(
1
6
n
+
31
30
)
(iii)
(
7
6
n
+
31
30
)
(iv)
(
1
6
n
+
6
5
)
(v)
(
1
6
n
+
67
30
)
Question
29
29.
The
t
3
of an A.P is
p
and
t
4
is
q
.
Find
t
20
and
t
n
.
(i)
(
−
16
p
+
17
q
)
,
(
−
p
n
+
4
p
+
q
n
−
3
q
)
(ii)
(
−
13
p
+
15
q
)
,
(
−
p
n
+
7
p
+
q
n
−
5
q
)
(iii)
(
−
17
p
+
18
q
)
,
(
−
p
n
+
3
p
+
q
n
−
2
q
)
(iv)
(
−
15
p
+
16
q
)
,
(
−
p
n
+
4
p
+
q
n
−
3
q
)
(v)
(
−
16
p
+
17
q
)
,
(
−
p
n
+
p
+
q
n
−
q
)
Question
30
30.
Determine k so that
(
4
k
+
7
)
,
(
8
k
+
5
)
and
(
k
+
6
)
are the consecutive terms of an A.P
(i)
5
11
(ii)
3
13
(iii)
3
11
(iv)
1
3
(v)
1
11
Question
31
31.
The product of two numbers is
280
and their arithmetic mean is
17
.
Find the two numbers.
(i)
(
15
,
21
)
(ii)
(
14
,
19
)
(iii)
(
17
,
20
)
(iv)
(
14
,
20
)
(v)
(
22
,
16
)
Question
32
32.
Find the common difference and next four terms of the
following A.P.
4
,
11
,
18
,
. . .
=
(i)
8
;
22
,
28
,
34
,
40
(ii)
8
;
28
,
36
,
44
,
52
(iii)
8
;
25
,
32
,
39
,
46
(iv)
7
;
25
,
32
,
39
,
46
Question
33
33.
Find the common difference and next four terms of the
following A.P.
2
9
,
25
72
,
17
36
,
. . .
=
(i)
1
1
8
;
(
-173
72
)
,
(
-59
18
)
,
(
-299
72
)
,
(
-181
36
)
(ii)
1
8
;
43
72
,
13
18
,
61
72
,
35
36
(iii)
1
1
8
;
259
72
,
85
18
,
421
72
,
251
36
(iv)
1
1
8
;
43
72
,
13
18
,
61
72
,
35
36
Question
34
34.
Find the sum of all natural numbers between 1 and 100 which are multiples of 8?
(i)
627
(ii)
623
(iii)
624
(iv)
621
(v)
625
Question
35
35.
Find the sum of all natural numbers between 100 and 200 which are multiples of 9?
(i)
1681
(ii)
1686
(iii)
1684
(iv)
1683
(v)
1682
Question
36
36.
Find the sum of the following A.P. series
(
2
x
+
5
y
)
,
(
−
3
x
+
10
y
)
,
(
−
8
x
+
15
y
)
. . .
to
15
terms
(i)
(
−
495
x
+
600
y
)
(ii)
(
−
422
x
+
520
y
)
(iii)
(
−
432
x
+
530
y
)
(iv)
(
−
520
x
+
520
y
)
(v)
(
−
516
x
+
530
y
)
Question
37
37.
Given a =
7
, d =
7
,
S
n
=
1470
, find
t
n
(i)
141
(ii)
137
(iii)
143
(iv)
140
(v)
139
Question
38
38.
Given a =
2
, d =
2
,
S
n
=
306
, find n
(i)
16
(ii)
15
(iii)
17
(iv)
20
(v)
18
Question
39
39.
Given a =
6
, d =
4
, n =
9
, find
t
n
(i)
38
(ii)
41
(iii)
36
(iv)
37
(v)
39
Question
40
40.
Given a =
9
, d =
5
, n =
18
, find
S
n
(i)
928
(ii)
926
(iii)
925
(iv)
930
(v)
927
Question
41
41.
Given
t
n
=
42
, n =
10
,
S
n
=
240
, find a
(i)
3
(ii)
6
(iii)
9
(iv)
7
(v)
5
Question
42
42.
Given
t
n
=
65
, n =
11
,
S
n
=
385
, find d
(i)
6
(ii)
7
(iii)
5
(iv)
3
(v)
8
Question
43
43.
Given
t
n
=
67
, d =
4
, n =
16
, find a
(i)
8
(ii)
6
(iii)
7
(iv)
4
(v)
9
Question
44
44.
Given
t
n
=
62
, d =
4
, n =
15
, find
S
n
(i)
507
(ii)
509
(iii)
511
(iv)
513
(v)
510
Question
45
45.
Given
t
n
=
127
, a =
8
, n =
18
, find
S
n
(i)
1216
(ii)
1214
(iii)
1218
(iv)
1215
(v)
1213
Question
46
46.
Given
t
n
=
36
, a =
6
, n =
16
, find d
(i)
3
(ii)
4
(iii)
2
(iv)
1
(v)
-1
Question
47
47.
Find
t
n
of the A.P
8
,
12
,
16
,
. . .
(i)
(
4
n
+
12
)
(ii)
(
4
n
+
8
)
(iii)
(
3
n
+
4
)
(iv)
(
4
n
+
4
)
(v)
(
7
n
+
4
)
Question
48
48.
If
S
40
and
S
20
of an A.P. are
1760
and
480
respectively, then
S
60
=
(i)
3840
(ii)
3842
(iii)
3841
(iv)
3838
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)
1
(ii)
3
2
(iii)
2
3
(iv)
(
-3
4
)
(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)
(
n
−
1
)
(
a
+
b
)
(iii)
(
a
−
b
)
(
n
+
1
)
(iv)
(
b
−
a
)
(
n
+
1
)
(v)
(
b
−
a
)
(
n
−
1
)
Question
51
51.
The sum of first n natural number is
(i)
(
n
)
(
n
+
1
)
2
(ii)
n
2
(
n
+
1
)
2
4
(iii)
(
n
−
1
)
(
n
+
1
)
2
(iv)
(
n
)
(
n
+
1
)
(
2
n
+
1
)
6
(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
125
and the largest angle is
175
,
then the number of sides of the polygon is
(i)
11
(ii)
12
(iii)
13
(iv)
10
(v)
15
Question
53
53.
If the
t
n
of an A.P is
(
2
n
+
9
)
, find
S
n
(i)
(
2
)
(
n
2
+
n
)
2
+
9
n
(ii)
(
6
)
(
n
2
+
n
)
2
+
4
n
(iii)
(
5
)
(
n
2
+
n
)
2
+
8
n
(iv)
(
9
)
(
n
2
+
n
)
2
+
7
n
(v)
(
2
)
(
n
2
+
n
)
2
+
6
n
Assignment Key
1) (iii)
2) (i)
3) (ii)
4) (ii)
5) (i)
6) (v)
7) (v)
8) (i)
9) (ii)
10) (i)
11) (i)
12) (v)
13) (iv)
14) (i)
15) (ii)
16) (iv)
17) (v)
18) (v)
19) (iii)
20) (v)
21) (ii)
22) (i)
23) (v)
24) (iv)
25) (v)
26) (iii)
27) (ii)
28) (ii)
29) (i)
30) (iii)
31) (iv)
32) (iv)
33) (ii)
34) (iii)
35) (iv)
36) (i)
37) (iv)
38) (iii)
39) (i)
40) (v)
41) (ii)
42) (i)
43) (iii)
44) (v)
45) (iv)
46) (iii)
47) (iv)
48) (i)
49) (i)
50) (iv)
51) (i)
52) (ii)
53) (i)
