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Sum

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

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#### Solution

For a, 7, b, 23, c… to be in AP

it has to satisfy the condition,

a_{5} – a_{4} = a_{4} – a_{3} = a_{3} – a_{2} = a_{2} – a_{1} = d

Where d is thecommon 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

Concept: Arithmetic Progression

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