Question

in an ap the sum of first four terms is 20 and the sum of first three terms is 12 then find the fourth term ofThe ap​

Answer 1

Step-by-step explanation:

To find the 4th term of an A.P

We need to find the 1st term (a)

and common difference (d)

Given: sum of 1st 4 terms is 20

Let us take the 4 terms as a-d, a, a+d, a+2d

So, a-d + a + a+d + a+2d = 20

Subtract -d with +d to get 0

And add a + a + a + a to get 4a

4a + 2d = 20 - (1)

Next, given sum of 1st 3 terms is 12

Let the 3 terms be a-d, a, a+d

Subtract -d with +d to get 0

And add a + a + a to get 3a

So, a-d + a + a+d = 12

= a + a + a = 12

= 3a = 12

= a = 12/3

a = 4

Now substitute a in (1)

4a + 2d = 20

= 4(4) + 2d = 20

= 16 + 2d = 20

2d = 20 - 16

2d = 4

d = 4/2

d = 2

Now we got both first term (a) = 4 and common difference (d) = 2

Therefore using aₙ formula

i.e. aₙ = a + (n - 1) d

4th term of A.P =

a₄= a + (4 - 1) d

a₄ = a + 3d

Apply the values of a and d respectively

a₄ = 4 + 3(2)

a₄ = 4 + 6

a₄ = 10

Therefore 4th term of A.P is 10