Question

the sum of 4th and 8th term of ap is 24 and the sum of 6th and 10th term 44 find ap

Answer 1

tn=a+(n-1)d

t4=a+3d
t8=a+7d

t4+t8=a+3d+a+7d
24=2a+10d
12=a+5d

t6=a+5d
t10=a+9d

t6+t10=a+5d+a+9d
44=2a+14d
22=a+7d
22=(a+5d)+2d
22=12+2d
2d=22-12
2d=10
d=5

a+5×5=12
a+25=12
a=12-25
a=-13

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.