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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