Question

two different AP common difference first term of a first ap is 2 more than the first term of the second AP if the 7th term of the first AP 28 and the 8th term of second ap is 29 then find the 2 difference ap
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Answer 1

♠ Given ♠

• Two different A.P have same common difference.
• 1st term of 1st A.P is 2 more than the 1st term of the 2nd A.P .
• 7th term of 1st first A.P, a₇ = 28 .
• 8th term of 2nd A.P, A₈ = 29.

♠ To Find ♠

The two different A.Ps.

♠ Solution ♠

• Let the first term of the second AP be x. Then the first term of the first AP is  x + 2.

• The common differences are the same, i.e. d.

a₇ = a + 6d

⇒ 28 = x + 2 + 6d

⇒ 28 = x + 2 + 6d

⇒ 26 = x + 6d

⇒ 6d + x = 26      . . .(i)

_____________

A₈ = A + 6d

⇒ 29 = x + 7d

⇒ 7d + x = 29      . . .(ii)

_____________

Subtracting equation (i) from equation (ii) :-

 7d + x = 29

- 6d + x = 26

___________

   d = 3

Therefore, the common difference of both the A.Ps is 3.

Putting the value of d in equation (i) :-

6d + x = 26

⇒ 6(3) + x = 26

⇒ 18 + x = 26

⇒ x = 26 - 18

⇒ x = 8

The first term of the 2nd AP is 8.

⇒ x + 2 = 10

The first term of the 1st AP is 10.

_____________

◘ Therefore, the A.Ps are :-

1st AP → 10, 10 + 3 = 13, 13 + 3 = 16, 16 + 3 = 19, ...

2nd AP → 8, 8 + 3 = 11, 11 + 3 = 14, 14 + 3 = 17, ...

Answer 2

❤Answer

1 AP = 10, 10+3 = 13, 13+3 = 16, 16+3 = 19

2 Ap = 8, 8+3 = 11, 11+3 = 14, 14+3 = 17

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