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

Let first term of an AP be a and d be common difference A/Q a+3d+a+7d=24  On solving 2a +10d=24take 2 common from LHS and RHS a+5d=12-------(1)  Now  a+5d+a+9d=44 Put eq. (1) 12+a+9d=44 a+9d=44-12 a+9d=32------(2)  from eq. (1)& (2) d=5 So, a =-13  So, AP be of form a, a+d, a+2d So first three terms of AP are -13, -8, -3  

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.