Mathematics - Sequence & Series Question with Solution | TestHub

Given set$=\left\{11,8,21,16,26,32,4\right\}$

Given an arithmetic series and a geometric series having the first four terms from the given set. 

Then, 

$\text{Geometric series} : 4,8,16,32,64,128,256,512,1024,2048,4096,8192$

$\text{Arithmetic series}: 11,16,21,26,31,36,...,256,....4096,...$

$T_n (G.P.)=4·2^{n-1}$

$T_n (A.P.)=11+5\left(n-1\right)=5n+6$

For common terms, $4·2^{n-1}=5n+6$

So, common terms are $16,256,4096$ only.