Question

Find a, b and c if it is given that the numbers a, 7, b, 23, c are in AP.
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Answer 1

Answer:

a = (-1)

b = 15

c = 31

Step-by-step explanation:

AP: a, 7, b, 23, c

Since they are in AP, their common difference (d) will be equal

d = 7 - a ---> (1)

d = b - 7 ---> (2)

d = 23 - b ---> (2)

d = c - 23 ---> (3)

From (2) and (3)

b - 7 = 23 - b

=> b + b = 23 + 7

=> 2b = 30

=> b = 30/2

=> b = 15

From (1) and (2)

7 - a = b - 7

=> a + b = 14

=> a + 15 = 14 {∵b = 15}

=> a = 14 - 15

=> a = (-1)

From (3) and (4)

23 - b = c - 23

=> b + c = 46

=> 15 + c = 46 {∵b = 15}

=> c = 46 - 15

=> c = 31