Question 64

Let 2$$^{nd}$$, 8$$^{th}$$ and 44$$^{th}$$, terms of a non-constant A.P. be respectively the 1$$^{st}$$, 2$$^{nd}$$ and 3$$^{rd}$$ terms of G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to

AP with a₁=1. 2nd term=1+d, 8th=1+7d, 44th=1+43d form GP.

$$(1+7d)^2=(1+d)(1+43d)$$. $$1+14d+49d^2=1+44d+43d^2$$. $$6d^2-30d=0$$. $$d(d-5)=0$$.

Non-constant: d=5. Sum of 20 terms: $$\frac{20}{2}(2+19\times5)=10(97)=970$$.

The answer is Option (4): 970.

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