Let a1, a2, a3, .....

Question

Let a1, a2, a3, ..... be an A.P. If $${{{a_1} + {a_2} + .... + {a_{10}}} \over {{a_1} + {a_2} + .... + {a_p}}} = {{100} \over {{p^2}}}$$, p $$\ne$$ 10, then $${{{a_{11}}} \over {{a_{10}}}}$$ is equal to :

Accepted Answer

$${{{{10} \over 2}(2{a_1} + 9d)} \over {{p \over 2}(2{a_1} + (p - 1)d)}} = {{100} \over {{p^2}}}$$

$(2{a_1} + 9d)p = 10(2{a_1} + (p - 1)d)$

$9dp = 20{a_1} - 2p{a_1} + 10d(p - 1)$

$$9p = (20 - 2p){{{a_1}} \over d} + 10(p - 1)$$

$${{{a_1}} \over d} = {{(10 - p)} \over {2(10 - p)}} = {1 \over 2}$$

$$\therefore$$ $${{{a_{11}}} \over {{a_{10}}}} = {{{a_1} + 10d} \over {{a_1} + 9d}} = {{{1 \over 2} + 10} \over {{1 \over 2} + 9}} = {{21} \over {19}}$$

Solutions · 1