Question

the 1st 8th and 22nd terms of an Ap are in three consecutive terms of a Go Find the common ratio of the To Given also that the sum of first 22ndterms of Ap is 275.Find its first term.

Answer 1

Step-by-step explanation:

Let a and d be the first term and common difference of the AP.

Given 1st, 8th and 32nd terms are consecutive terms of a GP.

Hence (a+7d)/a = (a+21d)/(a+7d)

Simplifying we get a = 7d……….(1)

Also given Sum to 22 terms of the AP = 385.

So 385 = (22/2)(a+a+21d) using the formula

S = (n/2)(a+l)

385 = 11(2a+21d)

35 = 35d since a=7d from (1)

So d = 1 and hence a = 7.

Common ratio = (a+7d)/a = 14/7 = 2

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Answer 2

Answer:

2

Step-by-step explanation:

A.P.: a,a+7d,a+21d

sum= n/2(2a+(n-1)d) ==> 385=11(2a+21d)

=> 2a+21d=55

a+7d/(a) = a+21d/(a+7d) -------eq1    {Reason common difference of g.p. should be same.}

So, a=7d      substitue a in eq.1

14d/7d=2

So, ans is 2