Question

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.​

Answer 1

Answer:

$\boxed{\sf The \: first \: three \: terms\: of \;the \: AP \:are \: -13,-8,-3}$

Step-by-step explanation:

Given

That sum of  4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44.

To Find

First three terms of the A.P.​

ANSWER

a(n) = a+ (n-1)d

∴ a(4) = a+(4-1)d

          = a + 3d $\longrightarrow$(1)

Now,

a(8) = a+ (8-1)d = a+7d $\longrightarrow$ (2)

Just like this ,

a(6) = a+ 5d $\longrightarrow$(3)

AND

a(10) = a+9d $\longrightarrow$ (4)

∵ It is given that , The sum of 4th and 8th terms  is 24.

a(4)+a(8) = 24

i.e a+3d+a+7d = 24[ From Equation 1 and 2]

2a +10d = 24 $\longrightarrow$ (5)

Similarly,

a(6)+a(10) = 44

a+5d+ a+ 9d = 44

2a+14d = 44

a = 44-14d $\longrightarrow$ (6)

         2

[Putting the value of a in Equation 5 in Equation 6]

2× $[\frac{ 44-14d}{2} ]$ + 10d = 24

44 - 14 d + 10d = 24

44 - 4d = 24

44-24 = 4d

20 = 4d

d = 20/4 = 5

Now to find the value of a substitute the value of d in Equation (6)

a = 44 - 14d

           2

a = 44 - 14 × 5

           2

a = -26/2 = -13

Now we have to find the first three terms of the AP

First Term,

a1 = a

So first term = -13

Second Term,

a2 = a+ d = -13+5 = -8

Third Term,

a(3) = a+ 2d = -13+ 2×5 = -3

Answer 2

Answer:

It is the correct answer.

Step-by-step explanation:

Hope this attachment helps you.