EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Progressions
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The
t
13
of an A.P. is
93
20
and the
t
12
is
89
20
.
Find
t
14
.
(i)
97
22
(ii)
97
20
(iii)
19
4
(iv)
97
18
(v)
99
20
Question
2
2.
Insert
2
arithmetic means between
6
5
and
57
35
.
(i)
37
35
,
32
35
(ii)
7
5
,
8
5
(iii)
57
35
,
72
35
(iv)
59
45
,
64
45
(v)
47
35
,
52
35
Question
3
3.
Determine
t
5
of an A.P whose
t
11
is
38
21
and common difference is
1
6
(i)
17
23
(ii)
17
19
(iii)
5
7
(iv)
17
21
(v)
19
21
Question
4
4.
Find the common ratio and next four terms of the following G.P.
1
4
,
(
-1
24
)
,
1
144
. . .
(i)
5
6
;
(
-1
864
)
,
1
5184
,
(
-1
31104
)
,
1
186624
(ii)
(
-1
6
)
;
(
-1
864
)
,
1
5184
,
(
-1
31104
)
,
1
186624
(iii)
5
6
;
(
-343
864
)
,
2401
5184
,
(
-16807
31104
)
,
117649
186624
(iv)
5
6
;
125
864
,
625
5184
,
3125
31104
,
15625
186624
Question
5
5.
The
t
n
of a G.P. =
(i)
(
a
)
(
(
r
)
n
−
1
)
(
r
−
1
)
(ii)
a
r
(
n
−
1
)
(iii)
r
a
(
n
−
1
)
(iv)
(
r
)
(
(
a
)
n
−
1
)
(
a
−
1
)
Question
6
6.
If a =
5
7
and d =
1
4
, find
t
5
of the A.P.
(i)
10
7
(ii)
4
3
(iii)
12
5
(iv)
12
7
(v)
2
Question
7
7.
Given
t
n
=
83
, d =
8
, n =
11
, find a
(i)
2
(ii)
3
(iii)
4
(iv)
6
(v)
0
Question
8
8.
Which term of the A.P.
5
,
14
,
23
,
. . .
is
68
?
(i)
t
7
(ii)
t
11
(iii)
t
9
(iv)
t
8
(v)
t
6
Question
9
9.
The sum of first three terms of a G.P. is
155
and
the sum of next three terms is
19375
.
Determine the G.P.
(i)
5
,
25
,
125
,
625
,
3125
,
15625
,
. . .
(ii)
2
,
28
,
125
,
625
,
3125
,
15625
,
. . .
(iii)
3
,
27
,
125
,
625
,
3125
,
15625
,
. . .
(iv)
7
,
23
,
125
,
625
,
3125
,
15625
,
. . .
(v)
8
,
22
,
125
,
625
,
3125
,
15625
,
. . .
Question
10
10.
Which term of the G.P.
4
,
8
,
16
,
. . .
is
64
?
(i)
t
2
(ii)
t
7
(iii)
t
5
(iv)
t
4
(v)
t
6
Question
11
11.
Given a =
1
, r =
0.90
find
t
4
and
t
n
of the G.P.
(i)
0.53
;
0.90
(
n
−
1
)
(ii)
0.73
;
0.90
(
n
−
1
)
(iii)
0.63
;
0.90
(
n
−
1
)
(iv)
0.93
;
0.10
(
n
−
1
)
(v)
0.83
;
1.90
(
n
−
1
)
Question
12
12.
How many terms of the A.P.
2
,
11
,
20
,
. . .
are needed to
make the sum
618
?
(i)
10
(ii)
11
(iii)
12
(iv)
13
(v)
15
Question
13
13.
If the
t
n
of an A.P is
(
n
+
1
)
, find
S
n
(i)
(
7
)
(
n
2
+
n
)
2
+
3
n
(ii)
(
1
)
(
n
2
+
n
)
2
+
7
n
(iii)
(
1
)
(
n
2
+
n
)
2
+
5
n
(iv)
(
5
)
(
n
2
+
n
)
2
+
8
n
(v)
(
1
)
(
n
2
+
n
)
2
+
n
Question
14
14.
The first term of the A.P.
3
8
,
1
2
,
5
8
,
3
4
,
7
8
,
. . .
=
(i)
3
4
(ii)
5
8
(iii)
1
2
(iv)
7
8
(v)
3
8
Question
15
15.
The product of two numbers is
3120
and their arithmetic mean is
56
.
Find the two numbers.
(i)
(
53
,
61
)
(ii)
(
52
,
59
)
(iii)
(
55
,
60
)
(iv)
(
62
,
54
)
(v)
(
52
,
60
)
Question
16
16.
How many terms of the A.P.
9
5
,
2
,
11
5
,
. . .
are needed to
make the sum
74
?
(i)
19
(ii)
23
(iii)
17
(iv)
20
(v)
21
Question
17
17.
Find the sum of first 51 natural numbers
(i)
1325
(ii)
1326
(iii)
1327
(iv)
1324
(v)
1328
Question
18
18.
If a =
16
15
and b =
58
45
,
the arithmetic mean of a and b =
(i)
53
45
(ii)
17
15
(iii)
53
47
(iv)
11
9
(v)
53
43
Question
19
19.
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
155
,
then the number of sides of the polygon is
(i)
12
(ii)
10
(iii)
8
(iv)
6
(v)
9
Question
20
20.
Find the value
' x '
so that
5
2
,
x
,
2
5
, are three consecutive terms of a G.P.
(i)
3
(ii)
1
(iii)
-1
(iv)
0
(v)
2
Question
21
21.
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)
2
3
(iii)
1
(iv)
(
-3
4
)
(v)
4
3
Question
22
22.
Given a =
2
, d =
6
, n =
13
, find
S
n
(i)
494
(ii)
491
(iii)
495
(iv)
496
(v)
493
Question
23
23.
The
t
7
of a G.P. is
1
2657205
and
t
6
is
1
295245
.
Find
t
3
.
(i)
1
403
(ii)
1
405
(iii)
1
135
(iv)
(
-1
405
)
(v)
1
407
Question
24
24.
Given
t
n
=
102
, a =
3
, n =
12
, find
S
n
(i)
628
(ii)
630
(iii)
629
(iv)
631
(v)
632
Question
25
25.
Find the common ratio and next four terms of the following G.P.
2
,
1.8
,
1.62
(i)
1.0
;
1.024
,
0.8192
,
0.65536
,
0.524288
(ii)
1.0
;
2.000
,
2.0000
,
2.00000
,
2.000000
(iii)
1.0
;
1.458
,
1.3122
,
1.18098
,
1.062882
(iv)
0.9
;
1.458
,
1.3122
,
1.18098
,
1.062882
Assignment Key
1) (ii)
2) (v)
3) (iv)
4) (ii)
5) (ii)
6) (iv)
7) (ii)
8) (iv)
9) (i)
10) (iii)
11) (ii)
12) (iii)
13) (v)
14) (v)
15) (v)
16) (iv)
17) (ii)
18) (i)
19) (v)
20) (ii)
21) (iii)
22) (i)
23) (ii)
24) (ii)
25) (iv)
