Find the A.P. whose 1st term is 100 and the sum of the first six terms is 5 times
the sum of the next six terms.
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Answer:
Let difference is d.
⇒a
1
+a
2
+a
3
+a
4
+a
5
+a
6
=5(a
7
+a
8
+a
9
+a
10
+a
11
+a
12
)
So by the formula, S
n
=
2
n
(a+l), where a &l are the first and last term of an AP, we have
6(
2
a
1
+a
6
)=5×6(
2
a
7
+a
12
)
⇒a
1
+a
6
=5(a
7
+a
12
)
⇒a+a+5d=5(a+6d+a+11d)
⇒2a+5d=10a+85d
⇒80d=−8a
⇒d= 10
−a
⇒
10
−100
⇒−10
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