Question

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

Answer 1

Given that sum of the 4th and 8th terms of an AP is 24.

⟹ a + 3d + a + 7d = 24

⟹ 2a + 10d = 24 ...(i)

Also the sum of the 6th and 10th term is 44.

⟹ a + 5d + a + 9d = 44

⟹ 2a + 14d = 44 ...(ii)

Subtracting equation (i) from equation (ii), we get:

4d = 20

⟹ d = 5

Substituting d = 5 in equation (i), we have:

2a + 10d = 24

⟹ 2a + 10 (5) = 24

⟹ 2a + 50 = 24

⟹ 2a = −26

⟹ a = −13

Hence first term of given A.P. is −13 and common difference is 5.

Answer 2

Answer:

- 13 , - 8 , - 3 .

Step-by-step explanation:

Let the first term a and common difference be d.

We know :

t_n = a + ( n - 1 ) d

t_4 = a + 3 d

t_8 = a + 7 d

We have given :

t_4 + t_8 = 24

2 a + 10 d = 24

a + 5 d = 12

a = 12 - 5 d ....( i )

t_6 = a + 5 d

t_10 = a + 9 d

: t_6 + t_10 = 44

2 a + 14 d = 44

a + 7 d = 22

a = 22 - 7 d ... ( ii )

From ( i ) and  ( ii )

12 - 5 d = 22 - 7 d

7 d - 5 d = 22 - 12

2 d = 10

d = 5

We have :

a = 12 - 5 d

a = 12 - 25

a = - 13

Now required answer as :

- 13 , - 8 , - 3 .

Finally we get answer.