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

1.	Find a, b and c such that the following numbers are in AP: a, 7, b, 23, c.
Answer» 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 equate, b – 7 = 23 – b 2b = 30 b = 15 (eqn 1) And, 7 – a = b – 7 From eqn 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

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

Answer»

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 equate,

b – 7 = 23 – b

2b = 30

b = 15 (eqn 1)

And,

7 – a = b – 7

From eqn 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