Question

The nth term of the A.P. a, 3a, 5a, ...... is
(a) na
(b) (2n - 1) a
(c) (2n + 1) a
(d) 2na​

Answer 1

Step-by-step explanation:

a = a , d = 3a - a = 2a

An = a + (n-1)d

= a + (n-1)2a

= a { 1 + 2(n-1) }

= a { 1 + 2n - 2}

= a(2n-1) = (2n-1)a

Answer 2

(b) The nth term of A.P is (2n-1)a

Step-by-step explanation:

Given: A.P. a, 3a, 5a, .....

To find: the nth term of the A.P.

As we know

The nth term of A.P. is given by

$a_n=a+(n-1)d$ where $a_n$ is nth term , a is first term , d is common difference and n is the number of terms

Therefore we have

First term a = a

Common difference d=  3a- a = 2a

$a_n= a+(n-1)(2a)\\\\\Rightarrow a_n= a+2an-2a\\\\\Rightarrow a_n = 2an-a\\\\\Rightarrow a_n= a(2n-1)$

Therefore the nth term of the A.P. is (2n-1)a

#Learn more

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