EduSahara™ Assignment
Name : Geometric Progression
Chapter : Progressions
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The first term of the G.P.
3
,
15
,
75
,
375
,
1875
,
. . .
=
(i)
375
(ii)
1875
(iii)
75
(iv)
15
(v)
3
Question
2
2.
The first term of the G.P.
1
8
,
1
32
,
1
128
,
1
512
,
1
2048
,
. . .
=
(i)
1
8
(ii)
1
128
(iii)
1
512
(iv)
1
32
(v)
1
2048
Question
3
3.
The common ratio of the G.P.
2
,
8
,
32
,
. . .
=
(i)
3
(ii)
6
(iii)
1
(iv)
4
(v)
5
Question
4
4.
The common ratio of the G.P.
8
5
,
8
45
,
8
405
,
. . .
=
(i)
1
11
(ii)
1
9
(iii)
1
7
(iv)
(
-1
9
)
(v)
1
3
Question
5
5.
The
t
5
of the G.P.
3
,
9
,
27
,
. . .
=
(i)
243
(ii)
242
(iii)
240
(iv)
244
(v)
245
Question
6
6.
The
t
7
of the G.P.
5
9
,
5
18
,
5
36
,
. . .
=
(i)
5
578
(ii)
1
192
(iii)
7
576
(iv)
5
576
(v)
5
574
Question
7
7.
Determine
t
8
of a G.P. whose
t
7
is
1
52488
and common ratio is
1
6
.
(i)
1
314928
(ii)
1
104976
(iii)
1
314926
(iv)
1
314930
(v)
(
-1
314928
)
Question
8
8.
The
t
3
of a G.P. is
32
and
t
5
is
512
.
Find
t
8
.
(i)
32768
(ii)
32766
(iii)
32767
(iv)
32769
(v)
32771
Question
9
9.
The
t
3
of a G.P. is
1
324
and
t
6
is
1
69984
.
Find
t
4
.
(i)
(
-1
1944
)
(ii)
1
648
(iii)
1
1944
(iv)
1
1946
(v)
1
1942
Question
10
10.
Which term of the G.P.
2
,
8
,
32
,
. . .
is
131072
?
(i)
t
8
(ii)
t
11
(iii)
t
9
(iv)
t
6
(v)
t
10
Question
11
11.
Which term of the G.P.
3
7
,
3
56
,
3
448
,
. . .
is
3
1835008
?
(i)
t
5
(ii)
t
8
(iii)
t
7
(iv)
t
6
(v)
t
10
Question
12
12.
The sum of first three terms of a G.P. is
28
while their product is
512
.
Find the G.P.
(i)
5
,
10
,
20
,
. . .
(ii)
7
,
14
,
28
,
. . .
(iii)
4
,
4
,
4
,
. . .
(iv)
4
,
0
,
0
,
. . .
(v)
4
,
8
,
16
,
. . .
Question
13
13.
The sum of first three terms of a G.P. is
73
80
while their product is
1
1000
.
Find the G.P.
(i)
4
5
,
2
15
,
1
45
,
. . .
(ii)
4
7
,
1
14
,
1
112
,
. . .
(iii)
6
5
,
3
20
,
3
160
,
. . .
(iv)
4
5
,
1
10
,
1
80
,
. . .
(v)
4
5
,
(
-1
10
)
,
1
80
,
. . .
Question
14
14.
Find the common ratio and next four terms of the following G.P.
8
,
1.6
,
0.32
(i)
0.3
;
0.008
,
0.0008
,
0.00008
,
0.000008
(ii)
0.2
;
0.064
,
0.0128
,
0.00256
,
0.000512
(iii)
0.3
;
0.216
,
0.0648
,
0.01944
,
0.005832
(iv)
0.3
;
0.064
,
0.0128
,
0.00256
,
0.000512
Question
15
15.
Find the common ratio and the next four terms of the
following G.P.
3
,
6
√
2
,
24
. . .
(i)
√
8
;
48
√
2
;
192
;
384
√
2
;
1536
(ii)
√
8
;
81
;
243
;
729
;
2187
(iii)
√
9
;
192
;
384
√
2
;
1536
;
3072
√
2
(iv)
√
8
;
6
√
2
;
12
;
12
√
2
;
24
(v)
√
9
;
48
√
2
;
192
;
384
√
2
;
1536
Question
16
16.
Find the value
' x '
so that
5
2
,
x
,
2
5
, are three consecutive terms of a G.P.
(i)
2
(ii)
1
(iii)
-2
(iv)
0
(v)
4
Question
17
17.
If a, b, c are three consecutive terms of an A.P, then which of the following are true?
a)
a
b
,
b
c
,
c
a
are in G.P.
b)
k
b
,
k
a
,
k
c
are in G.P.
c)
a
k
,
b
k
,
c
k
are in G.P.
d)
k
a
,
k
b
,
k
c
are in G.P.
(i)
{c,a,d}
(ii)
{d}
(iii)
{a,d}
(iv)
{b,d}
Question
18
18.
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)
pqs = 1
b)
q
2
=
ps
c)
s
2
=
pq
d)
p
2
=
qs
(i)
{c,b}
(ii)
{d,a,b}
(iii)
{b}
(iv)
{a,b}
Question
19
19.
Find the common ratio and next four terms of the following G.P.
(
-2
5
)
,
(
-1
5
)
,
(
-1
10
)
. . .
(i)
1
1
2
;
(
-27
20
)
,
(
-81
40
)
,
(
-243
80
)
,
(
-729
160
)
(ii)
1
1
2
;
(
-1
20
)
,
(
-1
40
)
,
(
-1
80
)
,
(
-1
160
)
(iii)
1
2
;
(
-1
20
)
,
(
-1
40
)
,
(
-1
80
)
,
(
-1
160
)
(iv)
1
1
2
;
1
20
,
(
-1
40
)
,
1
80
,
(
-1
160
)
Question
20
20.
Which term of the G.P.
2
,
2
√
2
,
4
. . .
is
256
?
(i)
t
13
(ii)
t
16
(iii)
t
18
(iv)
t
14
(v)
t
15
Question
21
21.
The
t
n
of a G.P. =
(i)
a
r
(
n
−
1
)
(ii)
r
a
(
n
−
1
)
(iii)
(
r
)
(
(
a
)
n
−
1
)
(
a
−
1
)
(iv)
(
a
)
(
(
r
)
n
−
1
)
(
r
−
1
)
Question
22
22.
Given a =
1
, r =
0.70
find
t
3
and
t
n
of the G.P.
(i)
0.39
;
0.70
(
n
−
1
)
(ii)
0.69
;
0.30
(
n
−
1
)
(iii)
0.49
;
0.70
(
n
−
1
)
(iv)
0.29
;
0.70
(
n
−
1
)
(v)
0.59
;
1.70
(
n
−
1
)
Question
23
23.
The sum of first three terms of a G.P. is
172
and
the sum of next three terms is
37152
.
Determine the G.P.
(i)
1
,
27
,
144
,
864
,
5184
,
31104
,
. . .
(ii)
7
,
21
,
144
,
864
,
5184
,
31104
,
. . .
(iii)
4
,
24
,
144
,
864
,
5184
,
31104
,
. . .
(iv)
2
,
26
,
144
,
864
,
5184
,
31104
,
. . .
(v)
6
,
22
,
144
,
864
,
5184
,
31104
,
. . .
Assignment Key
1) (v)
2) (i)
3) (iv)
4) (ii)
5) (i)
6) (iv)
7) (i)
8) (i)
9) (iii)
10) (iii)
11) (iii)
12) (v)
13) (iv)
14) (ii)
15) (i)
16) (ii)
17) (ii)
18) (iii)
19) (iii)
20) (v)
21) (i)
22) (iii)
23) (iii)
