Which term of the A.P. –29, –26, –23, ..., 61 is 16?

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Solution

Q.
Which term of the A.P. –29, –26, –23, ..., 61 is 16

1 11th

2 16th

3 10th

4 31st

Ans.
(2)

Given, $a = - 29$

$d = - 26 - (- 29) = - 26 + 29 = 3 \Rightarrow d = 3$

$a_{n} = 16$

Here we know, $a_{n} = a + (n - 1) d$

$\Rightarrow 16 = - 29 + (n - 1) 3$

$\Rightarrow 16 + 29 = (n - 1) 3 = 15$

$\Rightarrow n - 1 = \frac{45}{3} = 15$

$\Rightarrow 15 = n - 1 \Rightarrow n = 16$

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