Question

for what value of p the terms 2p+1,13,5p-3 are in ap

Answer 1

Let the first term of an AP be a

Let the common difference be d.

Then the AP should be like this:

a , a+d , a+d+d

==> a,  a+d,  a+2d

We see that 1st term + 3rd term = 2 * 2nd term

==>Proof

==> a is the first term

==> a+2d is the third term

Adding them gives:

==> a + a + 2d

==> 2a+2d

==> 2(a+d)

But a+d is the second term:

Hence 1st term + 3rd term = 2 * 2nd term.

Here to be in AP,

2p+1 + 5p-3 = 2 * 13

==> 7p - 2 = 26

==> 7p = 28

==>p=28/7

==>p=4

The value of p must be 4.

Then only will the numbers be in AP

Hope it helps

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