Question

the sum of the 4th term and 8 th of an Ap is 24 and the sum of the 6th and 10th term is 44.find the first three terms of ap

Answer 1

Given,
a + 3d + a + 7d = 24
2a + 10d = 24
a + 5d = 12......(I)

a + 5d + a + 9d = 44
2a + 14d = 44
a + 7d = 22.......(II)

From (I) and (II)
d = 5 and a = -13

Now, first three terms 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.