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The 3rd and 9th term of an arithmetic progression are -8 and 10 respectively. What is the 16th term?

A. 34 B. 28 C. 25 D. 31 Answer: Option D
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Solution(By Apex Team)

Let the first term of an AP = a and the common difference = d 3th term of AP = A3 = a + 2d = -8 ……(1) 9th term = A9 = a + 8d = 10 …… (2) Subtracting equation (1) from (2), we get : ⇒ 8d – 2d = 10 – (-8) ⇒ 6d =18 ⇒ d = $\Large\frac{18}{6}$ = 3 $\begin{array}{l}\text{ Substituting it in equation (2), }\\ \begin{aligned}\Rightarrow a&=10-8(3)\\ &=10-24\\ &=-14\end{aligned}\end{array}$ $\begin{array}{l}\therefore16^{\text{th }}\text{ term }=\mathrm{A}_{16}=\mathrm{a}+15\mathrm{~d}\\ =-14+15(3)\\ =-14+45\\ =31\end{array}$

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