Question

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:

answer is this -13,-8,-3

Answer 2

Answer:

• First three terms of AP are -13, -8, -3.

Step-by-step explanation:

Given:

• Sum of 4th and 8th term of Ap = 24
• Sum of 6th and 10th term of Ap = 44

To Find:

• First three term of AP.

Now, it is given that,

=> a₄ + a₈ = 24

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

=> 2a + 10d = 24 ......(1)

Now,

=> a₆ + a₁₀ = 44

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

=> 2a + 14d = 44 ......(2)

Now, we will solve these equations by substitution method,

=> 2a + 10d = 24

=> 2a = 24 - 10d

=> a = (24 - 10d)/2

Now, put the value of 'a' in equation (2),

=> 2a + 14d = 44

=> 2[(24 - 10d)/2] + 14d = 44

=> (48 - 20d)/2 + 14d = 44

=> (48 - 20d + 28d)/2 = 44

=> 48 - 20d + 28d = 88

=> 8d = 40

=> d = 40/8

=> d = 5

Now, put the value of 'd' in equation (1),

=> 2a + 10d = 24

=> 2a + 50 = 24

=> 2a = -26

=> a = - 13

Now, we will calculate first three terms,

=> a₁ = -13

=> a₂ = a + d = -13 + 5 = -8

=> a₃ = a + 2d = -13 + 10 = -3

Hence, First three terms of AP are -13, -8, -3....