Question

if a + 1, 2A + 1, 4a -1 are in AP then find the value of a

Answer 1

Solution:

Given that a+1,2a+1 and 4a-1 are in A.P.

Let 'd' denote the common difference of given sequence.

Now,

Common difference:

Second term - first term

=>d=(2a+1)-(a+1)

=2a+1-a-1

=a..................[1]

Also,

Common Difference:

Third term- second term

=>d=(4a-1)-(2a+1)

=4a-1-2a-1

=2a-2................[2]

From [1] and [2],we obtain;

a=2a-2

=>a=2

Putting a=2 in the A.P.,we get:

3,5,7,.................