EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Progressions
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Which term of the G.P.
1
9
,
1
27
,
1
81
,
. . .
is
1
2187
?
(i)
t
7
(ii)
t
9
(iii)
t
6
(iv)
t
5
(v)
t
3
Question
2
2.
Determine
t
19
of an A.P whose
t
15
is
31
and common difference is
2
(i)
41
(ii)
40
(iii)
38
(iv)
37
(v)
39
Question
3
3.
Insert
2
arithmetic means between
3
and
21
.
(i)
12
,
21
(ii)
7
,
11
(iii)
9
,
15
(iv)
10
,
17
(v)
8
,
13
Question
4
4.
If the
t
n
of an A.P is
(
3
n
+
1
)
, find
S
n
(i)
(
2
)
(
n
2
+
n
)
2
+
2
n
(ii)
(
3
)
(
n
2
+
n
)
2
+
n
(iii)
(
9
)
(
n
2
+
n
)
2
+
n
(iv)
(
9
)
(
n
2
+
n
)
2
+
8
n
(v)
(
8
)
(
n
2
+
n
)
2
+
6
n
Question
5
5.
How many terms of the A.P.
9
7
,
10
7
,
11
7
,
. . .
are needed to
make the sum
117
7
?
(i)
9
(ii)
6
(iii)
12
(iv)
8
(v)
10
Question
6
6.
The
t
n
of a G.P. =
(i)
(
r
)
(
(
a
)
n
−
1
)
(
a
−
1
)
(ii)
a
r
(
n
−
1
)
(iii)
(
a
)
(
(
r
)
n
−
1
)
(
r
−
1
)
(iv)
r
a
(
n
−
1
)
Question
7
7.
Find the sum of all natural numbers between 100 and 200 which are multiples of 6?
(i)
2549
(ii)
2553
(iii)
2550
(iv)
2551
(v)
2547
Question
8
8.
Find
t
10
of the A.P.
3
,
12
,
21
,
. . .
=
(i)
84
(ii)
83
(iii)
82
(iv)
85
(v)
86
Question
9
9.
Determine
t
4
of a G.P. whose
t
7
is
1
236196
and common ratio is
1
9
.
(i)
1
108
(ii)
1
326
(iii)
1
322
(iv)
1
324
(v)
(
-1
324
)
Question
10
10.
Find
S
25
of the A.P.
7
,
10
,
13
,
. . .
=
(i)
1078
(ii)
1072
(iii)
1076
(iv)
1074
(v)
1075
Question
11
11.
Determine
t
20
of an A.P whose
t
6
is
39
10
and common difference is
1
2
(i)
111
10
(ii)
109
12
(iii)
109
10
(iv)
109
8
(v)
107
10
Question
12
12.
The common difference of the A.P.
3
,
5
,
7
,
. . .
=
(i)
-1
(ii)
3
(iii)
4
(iv)
1
(v)
2
Question
13
13.
If a =
38
and b =
54
,
the arithmetic mean of a and b =
(i)
48
(ii)
45
(iii)
47
(iv)
44
(v)
46
Question
14
14.
Which term of the G.P.
2
,
2
√
2
,
4
. . .
is
64
√
2
?
(i)
t
10
(ii)
t
14
(iii)
t
12
(iv)
t
13
(v)
t
11
Question
15
15.
Find the common difference and next four terms of the
following A.P.
5
,
9
,
13
,
. . .
=
(i)
5
;
20
,
25
,
30
,
35
(ii)
4
;
17
,
21
,
25
,
29
(iii)
5
;
17
,
21
,
25
,
29
(iv)
5
;
14
,
17
,
20
,
23
Question
16
16.
If a =
1
6
and d =
1
3
, find
t
6
of the A.P.
(i)
3
2
(ii)
11
8
(iii)
11
4
(iv)
13
6
(v)
11
6
Question
17
17.
Given
t
n
=
35
, n =
9
,
S
n
=
171
, find d
(i)
6
(ii)
2
(iii)
5
(iv)
4
(v)
3
Question
18
18.
The
t
5
of the G.P.
2
,
10
,
50
,
. . .
=
(i)
1249
(ii)
1253
(iii)
1250
(iv)
1251
(v)
1247
Question
19
19.
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
4
)
(iii)
2
3
(iv)
4
3
(v)
3
2
Question
20
20.
If the nth ,(n+3)rd and (n+6)th term of a G.P. are p, q and s respectively, then which of the following are true?
a)
q
2
=
ps
b)
pqs = 1
c)
s
2
=
pq
d)
p
2
=
qs
(i)
{b,a}
(ii)
{a}
(iii)
{c,a}
(iv)
{d,b,a}
Question
21
21.
The
t
7
of a G.P. is
8192
and
t
4
is
128
.
Find
t
3
.
(i)
33
(ii)
34
(iii)
30
(iv)
32
(v)
31
Question
22
22.
The first term of the G.P.
5
6
,
5
54
,
5
486
,
5
4374
,
5
39366
,
. . .
=
(i)
5
486
(ii)
5
39366
(iii)
5
54
(iv)
5
6
(v)
5
4374
Question
23
23.
The sum of first three terms of a G.P. is
5
4
while their product is
125
2744
.
Find the G.P.
(i)
1
,
1
2
,
1
4
,
. . .
(ii)
5
7
,
(
-5
14
)
,
5
28
,
. . .
(iii)
5
9
,
5
18
,
5
36
,
. . .
(iv)
5
7
,
5
7
,
5
7
,
. . .
(v)
5
7
,
5
14
,
5
28
,
. . .
Question
24
24.
If there are n arithmetic means between a and b, the common difference d =
(i)
(
n
−
1
)
(
a
+
b
)
(ii)
(
b
−
a
)
(
n
+
1
)
(iii)
(
a
+
b
)
(
n
+
1
)
(iv)
(
b
−
a
)
(
n
−
1
)
(v)
(
a
−
b
)
(
n
+
1
)
Question
25
25.
Given
t
n
=
123
, d =
7
, n =
18
, find a
(i)
5
(ii)
4
(iii)
3
(iv)
1
(v)
6
Assignment Key
1) (iii)
2) (v)
3) (iii)
4) (ii)
5) (i)
6) (ii)
7) (iii)
8) (i)
9) (iv)
10) (v)
11) (iii)
12) (v)
13) (v)
14) (iii)
15) (ii)
16) (v)
17) (iv)
18) (iii)
19) (i)
20) (ii)
21) (iv)
22) (iv)
23) (v)
24) (ii)
25) (ii)
