Find the next number in the series. 8, 12, 24, 52.5, 157.5, ?

Concept: In this type of series, each term is produced by multiplying the previous term by a multiplier that itself increases by a fixed step every time — so the growth rate keeps accelerating instead of staying constant.

Application:

1. 12 ÷ 8 = 1.5, the multiplier for the first step.

2. 24 ÷ 12 = 2, the multiplier has risen by 0.5 from the previous step.

3. 157.5 ÷ 52.5 = 3, the multiplier has climbed further, still on the same +0.5-per-step rise (1.5, 2, ..., 3).

4. Continuing that same +0.5 increase, the multiplier for the next step becomes 3.5.

5. 157.5 × 3.5 = 551.25, the next number in the series.

Cross-check: 551.25 ÷ 157.5 = 3.5, exactly one step above the multiplier of 3 used for the previous term — consistent with the steady +0.5 rise running through the series.