We have given a series of AP 2p-1, 3p+1, 11 and we asked to find the value of p for which given series form in AP and also asked to find the numbers.
Book – RS AGGARWAL
class 10, Arithmetic Progression, chapter 5A, question no 4
Rajan@2021Guru
Find the value of p for which the numbers 2p-1, 3p+1, 11 are in AP. Hence, find the numbers.
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If the numbers a,b and c are in AP, then
b-a=c-b
⇒2b=a+c
The given three numbers (2p-1),(3p+1) and 11 are in AP.
Then,
2(3p+1)=(2p−1)+11
⇒6p+2=2p−1+11
⇒6p+2=2p+10
⇒6p−2p=10−2
⇒4p=8
⇒p=8/4
⇒p=2
So, the value of p is 2.
Then, the given numbers be
2×2−1,3×2+1,11
4−1,6+1,11
3,7,11