Class 11

Math

Algebra

Sequences and Series

If $X+3$ is the geometric mean between $X+1$ and $X+6,$ then find $X.$

- 2
- 3
- 4
- 5

**Correct Answer: ** Option(b)

**Solution: **Since $(X+3)$ is the geometric mean between $(X+1)$ and $(X+6)$, therefore,

$(X+3)_{2}=(X+1)(X+6)$

$⇒X_{2}+6X+9=X_{2}+7X+6$

$⇒6X+9=7X+6$

$⇒7X−6X=9−6$

$⇒X=3$