Question

(1) Find the AP whose first 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 1

Answer:

Here a=100

Let difference is d.

⇒a1+a2+a3+a4+a5+a6=5(a7+a8+a9+a10+a11+a12)

So by the formula, Sn=2n(a+l), where a&l are the first and last term of an AP, we have

6(2a1+a6)=5×6(2a7+a12)

⇒a1+a6=5(a7+a12)

⇒a+a+5d=5(a+6d+a+11d)