Question

If $2/3,K,5/8$ are in $AP$, then value of is

• A. $15$
• B. $21$
• C. $12$
• D. $31/48$

Answer 1

The correct option is D $31/48$

Given A.P series: $\frac{2}{3},K,\frac{5}{8}$

let a = first term $a=\frac{2}{3}$

b = second term=$K$;

c = third term=$\frac{5}{8}$;

Since, given three terms are in A.P;

$d=b-a=c-b$.....(where d = common difference)

$K-\frac{2}{3}=\frac{5}{8}-K$

$2K=\frac{2}{3}+\frac{5}{8}$

$2K=\frac{15+16}{24}$

$2K=\frac{31}{24}$

$K=\frac{31}{48}$

The required value of K is $\frac{31}{48}$

Option (D) is correct.