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

Solution:

For a, 7, b, 23, c… to be in AP it should 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)

By equating,

b - 7 = 23 - b

2b = 30

b = 15 (equation 1)

And,

7 - a = b - 7

Substituting b value in equation 1

7 - a = 15 - 7

a = - 1

So we get,

c - 23 = 23 - b

c - 23 = 23 - 15

c - 23 = 8

c = 31

Here a = - 1

b = 15

c = 31

Therefore, the sequence - 1, 7, 15, 23, 31 is an AP.

✦ Try This: Find a, b and c such that the following numbers are in AP: a, 3, b, 25, c

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 4

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

Summary:

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. a, b and c is -1, 15 and 31 in the AP: a, 7, b, 23, c

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