The nth term of the AP a, 3a

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Solution

Q.
The $n^{t h} t e r m o f t h e A P a, 3 a, 5 a, is :$

1 $n a$

2 $(2 n - 1) a$

3 $(2 n + 1) a$

4 $2 n a$

Ans.
(2)

Given AP is $a, 3 a, 5 a, \dots$ where first term $= a a n d d = 3 a - a = 2 a .$

$∴ I t s n^{t h} t e r m, a_{n} = a + (n - 1) d = a + (n - 1) \times 2 a \Rightarrow a_{n} = a + 2 a n - 2 a = 2 a n - a = a (2 n - 1)$

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