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 3 terms of on ap

Answer 1

Answer:

Hello there!

Step-by-step explanation:

Let assume a, a+d, a+2d........are the terms of AP.

Acc to the question:

4th Term = a+3d , 8th Term = a+7d, 6th = a+5d , 10th = a+9d.

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

=> 2a + 10d = 24   ......... (1

2nd condition, similarly:

2a + 14d = 44  ..........(2

Solving 1 & 2 by the method of elimination, we get:

d=5, a= -13

series will be, -13, -8, -3

Hope it helps!

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.