Question

The sum of 4th and 8th term of an ap is 24 and the sum of 6th and 10th term is 44 find the sum of first ten terms of the ap

Answer 1

a+3d+a+7d=24

= 2a+10d=24

now dividing the equation by 2 we get,

a+5d=12  ....................... equation 1

Also given,

a+5d+a+9d=44

= 2a+14d=44

now diving the equation throughout by 2 we get,

a+7d=22  .........................  equation 2

Now equation equation 1 and 2

we get

d=5 and a=-13

therfore the a.p=-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.