in a sequence of 21 terms the first 11 terms are in AP with common difference 2 and the last - Maths - Continuity and Differentiability

Question

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 of the AP is equal to the middle term of the GP
, then the middle term of the entire sequence ?

Aman Choubey · Accepted Answer

Dear Student,The first 11 term are in AP with common difference d=2 and first term is aThen the middle term of A
P  is the 6th term i e
     a+n-1d=a+6-12=a+10Let the G
P
 first term is P and common ratio r=2Then middle term of G
P i e
 16th term of sequence or 6th term of G
P  can be written as= prn-1=P 26-1=P
25since middle term of A P
=middle term of G P Therefore a+10=P
25…………………1Also 11th term of A
P =1st term of G P Therefore a+10
2=Pa+20=P…………………2Solving 1 and 2 givesP=-1031 and a=-63031Middle term of the sequence is the 11th term of A
P  or 1st term of G P i e
   P=-1031Regards

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 of the AP is equal to the middle term of the GP , then the middle term of the entire sequence ?