Question

The nth term of a sequence is defined to be $4n+3$. The $50$th term is how much greater than the $45$th term?

• A. $5$
• B. $16$
• C. $20$
• D. $23$
• E. $24$

Answer 1

The correct option is C $20$

Given that

$n^{th}$ term of the sequence is $4n$ $+$ $3$.

Let $f\left(n\right)$ denote the $n^{th}$ term of the sequence

$f\left(n\right)$ $=$ $4n$ $+$ $3$

To find the difference between ${50}^{th}$ term and ${45}^{th}$ term,

$f\left(50\right)$ $=$ $4$ $\times$ $50$ $+$ $3$

$=$ $203$

$f\left(50\right)$ $=$ $203$

$f\left(45\right)$ $=$ $4$ $\times$ $45$ $+$ $3$

$=$ $183$

$f\left(45\right)$ $=$ $183$

Difference between ${50}^{th}$ term and ${45}^{th}$ term $=$ $f\left(50\right)$ $-$ $f\left(45\right)$

$=$ $203$ $-$ $183$

$=$ $20$

Therefore, the difference between ${50}^{th}$ term and ${45}^{th}$ term is ${}^{\prime }{20}^{\prime }$.