If (2p - 1), 7, 3p are in AP, find the value of p.

1.	If (2p - 1), 7, 3p are in AP, find the value of p.
Answer» Let (2p - 1), 7 and p be three consecutive terms of an AP. Then 7-(2p - 1) = 3p - 7 \(\Rightarrow\) 5p = 15 \(\Rightarrow\) p = 3 ∴ When p = 3,(2p - 1), 7 and 3p form three consecutive terms of an AP. If 2p-1,7,3p are in AP we have 7-(2p-1) = 3p - 7 which gives 7 - 2p + 1 = 3p - 7 That is 5p=8+7 5p=15 p=3

Answer»

Let (2p - 1), 7 and p be three consecutive terms of an AP.

Then 7-(2p - 1) = 3p - 7

\(\Rightarrow\) 5p = 15

\(\Rightarrow\) p = 3

∴ When p = 3,(2p - 1), 7 and 3p form three consecutive terms of an AP.

If 2p-1,7,3p are in AP we have

7-(2p-1) = 3p - 7

which gives 7 - 2p + 1 = 3p - 7

That is 5p=8+7

5p=15

p=3

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