Suppose [a_1, a_2, , a_n], ..

Question

Suppose $$a_{1}, a_{2}, \ldots, a_{n}$$, .. be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the progression is $5: 17$

Accepted Answer

$$\because$$ a1, a2, .... an be an A.P of natural numbers and

$${{{S_5}} \over {{S_9}}} = {5 \over {17}} \Rightarrow {{{5 \over 2}[2{a_1} + 4d]} \over {{9 \over 2}[2{a_1} + 8d]}} = {5 \over {17}}$$

$$ \Rightarrow 34{a_1} + 68d = 18{a_1} + 72d$$

$$ \Rightarrow 16{a_1} = 4d$$

$$\therefore$$ $d = 4{a_1}$

Solutions · 1