Question

Find a, b and c such that the following numbers are in AP: a, 7, b, 23, c.

Answer 1

For a, 7, b, 23, c... to be in AP

It has to satisfy the condition,

a₅ – a₄ = a₄ – a₃ = a₃ – a₂ = a₂ – a₁ = d

Where d is the common difference

7 – a = b – 7 = 23 – b = c – 23  ...(1)

Let us equation,

b – 7 = 23 – b

2b = 30

b = 15   ...(Equation 1)

And,

7 – a = b – 7

From equation 1

7 – a = 15 – 7

a = – 1

And,

c – 23 = 23 – b

c – 23 = 23 – 15

c – 23 = 8

c = 31

So a = – 1

b = 15

c = 31

Then, we can say that, the sequence – 1, 7, 15, 23, 31 is an AP.