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The 3rd and 8th term of an arithmetic progression are -13 and 2 respectively. What is the 14th term?

A. 23 B. 17 C. 20 D. 26 Answer: Option C
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Solution(By Apex Team)

Let the first term of an AP = a and the common difference = d 3rd term of AP = A3 = a + 2d = -13 …… (1) 8th term = A8 = a + 7d = 2 …… (2) Subtracting equation (1) from (2), we get : ⇒ 7d – 2d = 2 – (-13) ⇒ 5d = 15 ⇒ d = $\Large\frac{15}{5}$ = 3 Substituting it in equation (2) ⇒ a = 2 – 7(3) = 2 – 21 = -19 ∴ 14th term = A14 = a + 13d = -19 + 13(3) = -19 + 39 = 20

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