An Arithmetic progression consists of 20 terms of which 4th term is 16 and the last term is 208. Find the 15th term

146

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147

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148

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149

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Solution

The correct option is C 148
Given that, $n = 20$
$a_{4} = 16; a_{20} = 208$
Applying the nth term formula,
$a_{n} = a + (n - 1) d$
$a_{4} = a + (4 - 1) d$
$a_{4} = a + 3 d$ ......... (1)
$a_{20} = a + (20 - 1) d$
$208 = a + 19 d$ ....... (2)
subtracting equation (1) & (2) we get,
$16 = a + 3 d$
$208 = a + 19 d$
(-) (-) (-)
-----------------
$- 192 = - 16 d$
$d = \frac{- 192}{- 16} = 12$
Put the value of d in equation (1)
$16 = a + 3 (12)$
$16 - 36 = a$
$a = - 20$
$a_{15} = a + (15 - 1) d$
$= - 20 + (14) 12$
$= - 20 + 168 \Rightarrow 148$
Therefore, 15th term is 148.

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