Number series – determine the next term: 0, 5, 60, 615, ?

Introduction / Context:
Some series grow by a “concatenate-like” arithmetic: multiply by a base and then add a steadily increasing addend. Spotting the stable multiplier and the linear growth in the addend reveals the next term quickly.

Given Data / Assumptions:

• Series: 0, 5, 60, 615, ?
• Values suggest repeated multiplication by 10, followed by adding a multiple of 5.

Concept / Approach:
Test the hypothesis: each term = previous term * 10 + k, with k increasing by a constant step. Check the successive k values to confirm a linear pattern.

Step-by-Step Solution:
0 → 5: 0*10 + 5 = 5 (k = 5)5 → 60: 5*10 + 10 = 60 (k = 10)60 → 615: 60*10 + 15 = 615 (k = 15)k values are 5, 10, 15 → arithmetic progression +5. Next k = 20.Next term = 615*10 + 20 = 6170.

Verification / Alternative check:
The stable ×10 multiplier is the simplest consistent base; any other option that does not equal 6150 + 20 breaks the linear +5 addend growth.

Why Other Options Are Wrong:
6030/6130/6000 do not follow the +5 progression in the additive part (they would correspond to k = −120, −20, or −150 respectively, none of which match the established arithmetic).

Common Pitfalls:
Interpreting “615” as a concatenation artifact rather than 60*10+15; the arithmetic model explains all transitions precisely.

Final Answer:
6170