Q254 / 270 · NDA 2022 (Phase 1) · Mathematics

What is the arithmetic mean of 50 terms of an AP with first term 4 and common difference 4 ?

  • A
    50
  • B
    51
  • C
    100
  • Correct answer
    D
    102

Solution

Given $\mathrm{a}=4, \mathrm{~d}=4$ and $\mathrm{n}=50$ hence $\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}[2 \mathrm{a}+(\mathrm{x}-1) \mathrm{d}]$ $\begin{aligned} & =\frac{50}{2}[2 \times 4+49 \times 4] \\ & =50[4+98] \\ & \text {Now } \bar{X}=\frac{S_n}{\mathrm{~h}}=\frac{50 \times 102}{50}=102\end{aligned}$

Hence, the correct answer is option: 'D'.

Relevant Questions