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Byju's Answer
Standard X
Mathematics
nth Term of an AP
If S 3=31 and...
Question
If S
3
= 31 and S
6
= 3906 then find a and r.
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Solution
We know that the sum of the first n
th
term of the G.P. is
S
n
=
a
(
r
n
-
1
)
r
-
1
for r > 1.
We know: S
3
= 31 and S
6
= 3906
Thus, we have:
S
3
=
a
(
r
3
-
1
)
r
-
1
=
31
.
.
.
.
.
(
1
)
S
6
=
a
(
r
6
-
1
)
r
-
1
=
3906
.
.
.
.
(
2
)
On
dividing
(
2
)
by
(
1
)
,
we
get
:
a
r
6
-
1
r
-
1
×
r
-
1
a
r
3
-
1
=
3906
31
⇒
r
3
2
-
1
r
3
-
1
=
126
⇒
r
3
+
1
r
3
-
1
r
3
-
1
=
126
⇒
r
3
+
1
=
126
⇒
r
3
=
125
⇒
r
3
=
(
5
)
3
⇒
r
=
5
Now
,
on
putting
r
=
5
in
(
1
)
,
we
get
:
a
5
3
-
1
5
-
1
=
31
a
×
124
4
=
31
a
=
31
×
4
124
=
1
Thus, we get:
a = 1 and r = 5
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