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in a sequence of 21 terms the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. if the middle term the AP is equal to the middle term of GP. Then the middle term of entire sequence is?

in a sequence of 21 terms the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. if the middle term the AP is equal to the middle term of GP. Then the middle term of entire sequence is?

Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
note that last term of the AP is equal to first term of the GP.
a11= a1+10*2= 20+a1
middle term is a6= a1+5*2
for gp, middle term is a11*2^5= 32a11= 32(20+a1)= a1+5*2
so 31a1=10-640=-630
or a1= -630/31
middle term of entire sequence is  20+a1
 20-630/31
-10/31

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