Question

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

Answer 1

Step-by-step explanation:

= (a+3d)+(a+7d)=24

2a+10d=24..........eq...(1)

=(a+5d)+(a+9d)=44

2a+14d=44.........eq..(2)

now subtract eq (1) from (2)

2a+14d=44

2a+10d=24

- - -.

4d=20

d=5

now put value of d in eq....(1)

2a +10d=24

2a+10*5=24

2a+50=24

2a=24-50

2a=-26

a= -13.........

ap formed will be

a= -13

a+d= -13 +5=-8

a+2d= -13 + 2 (5)

= -13+10= -3

hence ap is -13,-8,-3.................

thanks

hope its helpful...........

Answer 2

Hello !

Given:-

• $a_{4}$ + $a_{8}$ = 24
• $a_{6}$ + $a_{10}$ = 44.

To find:-

• first 3 terms of the A.P.

Solution:-

$\implies$ a+3d+a+7d = 24

$\implies$ 2a+10d = 24

$\implies$ a+5d = 12 .......... eq.1

$\implies$ a+5d+a+9d = 44

$\implies$ 2a+14d = 44

$\implies$ a+7d = 22 .......... eq.2

subtracting eq.1 from eq.2

$\implies$ a+7d-(a+5d) = 22-12

$\implies$ a+7d-a-5d = 10

$\implies$ 2d = 10

$\implies$ d = $\cancel\dfrac{10}{2}$ = 5

$\implies$ d = 5.

now, putting the value of d in eq.1

$\implies$ a+5d = 12

$\implies$ a+5(5) = 12

$\implies$ a+25 = 12

$\implies$ a = -13.

Hence, the terms are:-

-13, -8, -3..........