Question

The n th term of a sequence is na +

b. prove that the sequence is an

a. p. with common difference a

Answer 1

Solution:

Given: nth term of an A.P is an+b,.
that's : $a_n=an+b$

To prove: common difference between each term is a,
that's : d=a,.

Proof: when n=1 then,$a_n=a_1$

$a_1=a(1)+b$
$a_1=a+b$...(i)

when n=2,
$a_2=a(2)+b$
$a_2=2a+b$...(ii)

$d=a_2-a_1$
$d=(2a+b)-(a+b)$
$d=2a+b-a-b$
∴$d=a$ 
                                                   hence,proved
                                         Hope it Helps!