Question

If the numbers a, 7, b, 23, c are in AP, find a, b and c.

Answer 1

Given: The five numbers a, 7, b, 23, c are in arithmetic progression (AP), so consecutive differences are equal.

Step-wise calculation:

1. Let the common difference be d.

Then 7 – a = d, b – 7 = d, 23 – b = d, c – 23 = d.

2. Equate b – 7 and 23 – b:

b – 7 = 23 – b

⇒ 2b = 30

⇒ b = 15

3. Use 7 – a = b – 7:

7 – a = 15 – 7 = 8

⇒ a = 7 – 8

⇒ a = –1

4. Use 23 – b = c – 23:

23 – 15 = c – 23

⇒ 8 = c – 23

⇒ c = 31