Question : The 3rd and 8th terms of an Arithmetic progression are –14 and 1, respectively. What is the 11th term?
Option 1: 14
Option 2: 16
Option 3: 20
Option 4: 10
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Correct Answer: 10
Solution : Given: The 3 rd and 8 th terms of an Arithmetic progression are –14 and 1. Formula for $n^{th}$ term ⇒ $a +(n-1)d$, where $a$ = 1 st term, $d$ = common difference and $n$ = number of terms $3^{rd}$ term ⇒ $a +(3-1)d=–14$ ⇒ $a + 2d = – 14$ ---------------------------------(1) $8^{th}$ term ⇒ $a +(8-1)d=1$ ⇒ $a + 7d = 1$ ------------------------------------(2) Subtracting equation (1) from (2), we get, $⇒5d=15$ $\therefore d=3$ Putting this value in equation (1), we get, $a+2×3=-14$ $\therefore a=-20$ So, $11^{th}$ term = $-20 +(11-1)3=10$ Hence, the correct answer is 10.
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