Question

Find the value of p for which the numbers 2p-1,3p+1,11are in ap. Hence find the numbers

Answer 1

let a , b ,c are three terms of A.P

as we know that difference between two terms of an A.P will be equal , so now

difference ,b -a = c - b

2b = c + a ------(1)

now put , a = 2p - 1 ,b = 3p + 1 , c = 11 in equation (1) , we get

2 ( 3p + 1 ) = 11 + 2p - 1

6p + 2 = 10 + 2 p

6p - 2 p = 10 - 2

4p = 8

p = 2

hence value of p = 2

so now , a=2p - 1 = 2(2) - 1 = 3

b=3p + 1 = 3(2) + 1 = 7

c= 11

therefore three numbers of A.P are

3 ,7 and 11.

● hope it helps ●