Question

the sum of the 4th and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44.Find the first term and the common difference ​

Answer 1

Hey mate○□●■ , here is ur answer

▪ Given, ATQ 4th term +6th term =24

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

=> 2a + 10d= 24

=>a + 5d= 12.........(i)

▪ 6th term + 10th term=44

=> a + 5d + a + 9d =44

=> 2a + 14d = 44

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

From equations (i) and (ii)

=> a + 7d - a - 5d = 10

=> 2d = 10

=> d = 5

First term = > a

from equation (i) , a +5(5)= 12

a = 12-25= -13

♤♤♡♡◇◇♧♧ Hope it helps.... thank u

Answer 2

Answer:

a = - 13

d = 5

A.P. = - 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.