A GP in one AP

The general expression for this sequence is : 2^n + 2 where n = integer numbers starting from 1.

This is a mental ability problem.

The series is like this,

$3$ $3+2^{0}=4$ $4+2^{1}=6$ $6+2^{2}=10$ $10+2^{3}=18$ $18+2^{4}=34$ $....................$

Keep writing the numbers. The 10th term will be $258+2^{8}=514$

Hence, the answer will be $514+2^{9}=514+512=\boxed{1026}$

4-3=1=2° 6-4=2=2¹ 10-6=4=2² 18-10=8=2³ 34-18=16=2.2³

11th= 3+ (1+2+4+8+16+32+64+128+256+512)= 1026