Question

the sum of 4th and 8th term is 24 and the sum of 6th and 10th term is 44 find the AP​

Answer 1

a4 = a+3d

a8 = a+7d

a4+a8 = 24

a+3d+a+7d = 24

2a+10d = 24

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

a6 = a+5d

a10 = a+9d

a6+a10 = 44

a+5d+a+9d = 44

2a+14d = 44

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

Now solve these equations using any method that you learnt in chapter 1 and you will get d = 5 and a= -13.

Find a2, a3, a4,....... and you get the A.P.

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.