Question

18. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is
44. Find the first three terms of the ap

Answer 1

Answer:

- 13, -8, -3

Step-by-step explanation:

Let the first term be a and com. diff. be d.

nth term = a + (n - 1)d

In the question :

Case 1: 4th + 8th term is 24

=> (a + 3d) + (a + 7d) = 24

=> a + 5d = 12 ...(1)

Case 2: 6th + 10th term is 44

=> (a + 5d) + (a + 9d) = 44

=> a + 7d = 22 ...(2)

Subtracting (1) from (2), we get

=> (a + 7d) - (a + 5d) = 22 - 12

=> d = 5

Thus, in eqⁿ: a + 5(5) = 12 → a = - 13

Therefore, first three terms are:

a = - 13

a + d = -13 + 5 = -8

a + 2d = -13 + 5(2) = -3

First three terms are -13, -8, -3.

Answer 2

Given :-

The  sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is  44.

To Find :-

First three terms of the ap

Solution :-

We know that

aₙ = a + (n - 1)d

For 4th term

a₄ = a + (4 - 1)d

a₄ = a + 3d

For 8 th term

a₈ = a + (8 - 1)d

a₈ = a + 7d

Now

a + 3d + a + 7d = 24

2a + 10 = 24

2a + 10d/2 = 24/2

a + 5d = 12 (1)

For 6th term

a₆ = a + (6 - 1)d

a₆ = a + 5d

For 10th term

a₁₀ = a + (10 - 1)d

a₁₀ = a + 9d

a + 5d + a + 9d = 44

2a + 14d = 44

2a + 14d/2 = 44/2

a + 7d = 22 (2)

Now

Subtracting 2 and 1

(a + 7d) - (a + 5d) = 22 - 12

a + 7d - a - 5d = 10

2d = 10

d = 10/2

d = 5

Finding a

a + 7(5) = 22

a + 35 = 22

a = 22 - 35

a = -13

Terms of AP are given by

a = -13

a + d = -13 + 5 = -8

a + 2d = -13 + 2(5) = -10 + 10 = -3