Question

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

Answer 1

Let the first term of an A.P = a
and the common difference of the given A.P = d
As we know that
a n = a+(n-1) d
a 4 = a +( 4-1) d
a 4 = a+3d
Similarly ,
a 8 = a + 7 d
a 6 = a + 5 d
a 10 = a+ 9d
Sum of 4 th and 8th terms of an A.P = 24 ( given )
a 4 +a 8 = 24
a + 3d + a + 7d = 24
2a + 10 d = 24
a +5d = 12 .....................(i)
Sum of 6 th and 10 th term of an A.P = 44 ( given )
a 6 +a 10 = 44
a + 5d +a+ 9d = 44
2a + 14 =44
a + 7d = 22 .....................(ii)
Solving (i) & (ii)
a +7 d = 22
a + 5d = 12
- - -

2d = 10
d = 5
From equation (i) ,
a + 5d = 12
a + 5 (5) = 12
a+2 5= 12
a = - 13
a 2 = a+d = -13+5 = -8
a 3 = a 2 + d = -8+5 = -3
-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.