Question

The common difference of two different arithmetic progressions are equal.The first term of the

first progression is 3 more than the first term of second progression. If the 7th term of first

progression is 28 and 8th term of second progression is 29, then find the both different

arithmetic progressions.​

Answer 1

Step-by-step explanation:

Let the terms of the first AP be a1, a2, a3..

and the terms of the second AP be A1, A2, A3...

Let the common difference of the APs be d.

Given,

a1 = 3 + A1 ---(1)

a7 = 28

a1 + 6d = 28 ---(2)

Substituting eq 1 in eq 2

(3 + A1) + 6d = 28

A1 + 6d = 25 ---(3)

A8 = 29

A1 + 7d = 29 ---(4)

Subtracting eq 3 from eq 4

A1 + 7d = 29

A1 + 6d = 25

d = 4

Substituting d=4 in eq 2 and 4,

a1 + (6×4) = 28

a1 + 24 = 28

a1 = 4

& A1 + 7d = 29

A1 + (7×4) = 29

A1 + 28 = 29

A1 = 1

First progression: 4, 8, 12, 16, 20, 24, 28...

Second progression: 1, 5, 9, 13, 17, 21, 25, 29....