Step-by-step explanation:

Given:-

The sum of 4th and 8th term of Ap is 24 and the sum of 6th and 10TH term is 44.

To find:-

Find the three terms of the AP?

Solution:-

We know that

a is the FIRST term and d is the common difference of an AP then nth term = an = a+(n-1)d

4th term of the AP = a4 = a+(4-1)d

a4 = a+3d

6th term = a6 = a+5d

8th term = A8 = a+7d

10th term = a10 =a+9d

Now

Sum of 4th and 8 th terms = 24

=> a4+a8 = 24

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

=>2a+10d = 24

=>2(a+5d) = 24

=>a+5d = 24/2

a+5d = 12------------(1)

and Sum of 6th and 10th terms = 44

=>a6+a10 = 44

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

=>2a+14d =44

=>2(a+7d)=44

=>a+7d = 44/2

a+7d = 22---------(2)

On Subtracting (1) from (2) then

a+7d = 22

a+5d = 12

(-)

________

0+2d = 10

_________

=>2d = 10

=>d = 10/2

=>d = 5

On Substituting the value of d in (2) then

=>a+7(5)=22

=>a+35 = 22

=>a = 22-35

=>a = -13

We have a = -13 and d = 5

The first three terms of the AP are

a,a+d,a+2d

a= -13

a+d = -13+5 = -8

a+2d = -13+2(5)=-13+10=-3

Answer:-

The first three terms of the given AP are -13,-8,-3

Check:-

a4 = a+3d = -13+4(5)=-13+20=7

a8 = a+7d = -13+7(4)=-13+28=15

a4+a8 = 7+15 = 22

a6 = a+5d = -13+5(5)=-13+25=12

a10=a+9d = -13+9(5)=-13+45 = 32

a6+a10=12+32=44

Verified the given relations.

Used FORMULAE:-

• a is the first term and d is the common difference of an AP then nth term = an = a+(n-1)d