Question

P, Q and R are three consecutive terms in a geometric progression. If log P = k  and log R = m, then what is the value of 2log(PQR)?
1. 3(k + m)
2. 2(k + m)
3. 2(k - m)
4. 3(k - m)

Answer 1

Correct Answer - Option 1 : 3(k + m)

Calculation:

P, Q and R are three consecutive terms in a GP 

⇒ Q is the geometric mean of P and R

⇒ Q = (PR)^1/2

log(PQR) = log P + log Q + log R

⇒ log P + log (PR)^1/2 + log R

⇒ log P + (1/2) log (PR) + log R

⇒ log P + (1/2)(log P + log R) + log R

⇒ (3/2) × (log P + log R)

⇒ (3/2) × (k + m)

2log(PQR) = 2 × (3/2) × (k + m) = 3(k + m)

If P, Q and R are three consecutive terms in a Geometric progression, Q will be the geometric mean of P and R.

Q² = PR