Question

What is the difference between the sixth and the fifth terms of the sequence $2,4,7,...$ whose $n^{th}$ term is $n+2^{n-1}$ ?

• A. $2$
• B. $3$
• C. $6$
• D. $16$
• E. $17$

Answer 1

The correct option is E $17$

Given, $n^{th}$ term is $n+2^{n-1}$

The sixth term will be $=6+2^{6-1}=6+2^5=6+32=38$

The fifth term will be $=5+2^{5-1}=5+2^4=5+16=21$

Therefore, $\text{difference}=38-21=17$