find the first term whose first term is 100 and sum of first term is 5 times the sum of its next 6 term
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Answer:
Here a=100
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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