Question

if 2/5 , a and 4/5 are 3 consecutive term of an AP then the value of a is ___​

Answer 1

ANSWER:

Given:

• Three consecutive terms of an AP = 2/5, a, 4/5

To Find:

• Value of a.

Solution:

We are given that,

⇒ Three consecutive terms = 2/5, a, 4/5

We know that, for an AP, the common difference between 2 consecutive terms is equal.

That is,

⇒ a - 2/5 = d ------(1)

And,

⇒ 4/5 - a = d --------(2)

Equating (1) & (2),

⇒ a - 2/5 = 4/5 - a

Transposing -a to LHS,

⇒ a - 2/5 + a = 4/5

⇒ 2a - 2/5 = 4/5

Transposing -2/5 to RHS,

⇒ 2a = 4/5 + 2/5

⇒ 2a = (4 + 2)/5

⇒ 2a = 6/5

Transposing 2 to RHS,

⇒ a = 6/(5×2)

⇒ a = 6/10

Dividing the numerator and denominator by 2,

⇒ a = 3/5

Hence, the value of a is 3/5.