Question

What is the next number in the series $2,12,36,80,150,$?

• A. $263$
• B. $251$
• C. $284$
• D. $252$

Answer 1

The correct option is D

$252$

Step 1: Difference between the first and second term in the series.

The given series is $2,12,36,80,150$.

Take the difference between the first and second term to find the next term.

$\begin{array}{rcl}12–2& =& 10\\ 36–12& =& 24\\ 80–36& =& 44\\ 150–80& =& 70\end{array}$

Thus, the series of differences is $10,24,44,70$.

Step 2: Difference between the first and second term of the new series $10,24,44,70$.

Consider the fifth term of the series be $X$.

$$\begin{gathered} 24–10=14 \\ 44–24=20 \\ 70–44=26 \end{gathered}$$

Thus, new series of differences is $14,20,26$.

Step 3: Difference between the first and second term of the new series $14,20,26$.

Consider the fourth term of the series be $Y$.

$$\begin{gathered} 20–14=6 \\ 26–20=6 \end{gathered}$$

Thus, the difference is $6$, which is constant.

Step 4. Find the next term in the given series.

Add $6$ to the third term of the series of Step $2$ to find the value of $Y$.

$\begin{array}{rcl}Y& =& 26+6\\ & \Rightarrow & Y=32\end{array}$

Add $32$ to the fourth term of the series of Step $1$ to find the value of $X$.

$\begin{array}{rcl}X& =& 70+32\\ & \Rightarrow & X=102\end{array}$

Now, add $102$ to the fifth term of the given series to find the next term in the given series.

$150+102=252$

Hence, option (D) is correct.