Question

For what value of p, the following terms are three consecutive terms of an A.P. 4 /5 , p ,2.

Answer 1

Given:  ⅘, p, 2 will be consecutive terms of an AP

Here, first term = ⅘
Second term= p
third term = 2

Second term -  first term = third term -  second term

(p) - ⅘ =  2 - p
p + p = 2 + ⅘
2p = (2× 5 +4) /5
2p = (10+4)/5
2p = 14 / 5
p = 14/(5×2)

p = 7/5
Hence, the value of p is 7/5.

HOPE THIS WILL HELP YOU...

Answer 2

Here is the stepwise solution. I hope u find it useful
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As all three are terms of an AP,
(a+2d) - (a+d) = (a + d) - a
2 - p = p -4/5
2 + 4/5 = 2p
10/5 + 4/5 = 2p
14/5 = 2p
p = 7/5