Question

1. The numbers x + 3,2x + 1 and x-7 are in Arithmetic progression.
(1) Find the difference between the second term and the first term.
(ii) Find the difference between the third term and the second term.
(iii) Using the results of (i) and (ii), find the value of x and thus find the value of three numbers.​

Answer 1

a1 = x+3

a2 = 2x+1

a3 = x-7

a2-a1 = 2x+1-x-3 = x-2

a3-a1 = x-7-2x-1 = -x-8

Since a2-a1 = a3-a2 = d [Common Difference]

x-2 = -x-8

2x = 2-8 = -6

x = -3

Therefore, the numbers are

3-3 = 0

-6+1 = -5 and

-3-7 = -10

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