Q.

In a sequence of 21 terms the first 11 terms are in A.P. with common difference 2 and the last 11 terms are in G.P. with common ratio 2 . If the middle term of the A.P. is equal to the middle term of the G.P., then the middle term of the entire sequence is

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a

-1031

b

-63031

c

-3231

d

-32031

answer is A.

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Detailed Solution

Here common difference d=2, common ratio =2 Given, middle term of the A.P= middle term of the G.P ⇒a+(6-1)2=[a+(11-1)2]25⇒a=-63031∴middle term=a+10d=a+20                                          =-63031+20                                           =-1031
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In a sequence of 21 terms the first 11 terms are in A.P. with common difference 2 and the last 11 terms are in G.P. with common ratio 2 . If the middle term of the A.P. is equal to the middle term of the G.P., then the middle term of the entire sequence is