Question

the sum of the 4th and 8th is it 24 the sum of the 6th and 10th term is 44 find the first three terms of the AP

Answer 1

As we know that,

a n = a + (n − 1) d

a 4 = a + (4 − 1) d

a 4 = a + 3d

Similarly,

a 8 = a + 7d

a 6 = a + 5d

a 10 = a + 9d

Sum of 4th and 8th term =  24  (Given)

a 4 + a 8 = 24

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12.................... (i)

Sum of 6th and 10th term = 44  (Given)

a 6 + a 10 = 44

a + 5d + a + 9d = 44

2a + 14d = 44

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

Solving (i) and (ii), we get,



From equation (i), we get,

a + 5d = 12

a + 5 (5) = 12

a + 25 = 12

a = −13

a 2 = a + d = − 13 + 5 = −8

a 3 = a 2 + d = − 8 + 5 = −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.