Question

In an Arithmetic progression the sum of first four terms is 20 and the sum of first three terms is 12 then find the fourth term of the arithmetic progression.

Answer 1

Answer:

T₄ = 8

Step-by-step explanation:

Question:

In an Arithmetic progression the sum of first four terms is 20 and the sum of first three terms is 12 then find the fourth term of the arithmetic progression

let's find out the solution

Give the sum of first 4 terms of an A.P is 20

⇒ 4/2(a + a + 3d) = 20

⇒ 2a + 3d = 10 -----[1]

And the sum of first 3 terms is 12

⇒ 3/2(a + a + 2d) = 12

⇒ 2a + 2d = 8

∴ a + d = 4 -----[2]

Solve equation [1] & [2] we get,

$\red{\bold{2a + 3d = 10}}\\\\\red{\underline{\bold{a + d = 4}}}\\\\\red{\bold{2a + 3d = 10}}\\\\\red{\underline{\bold{_-2a + _-2d =_- 8}}}\\\\\green{\bold{d = 2}}$

Common difference = 2

Put 'd in [1] or [2]

→ a + d = 4

→ a + 2 = 4

→ a = 2

4'th term = a + 3d

→ 2 + (3*2) = 2 + 6 = 8

∴ T₄ = 8

Answer 2

Given:

Sum of first four terms of A.P., S₄=20

sum of first three terms of AP, S₃=12

To Find:

Find the fourth term T₄

Solution:

Arithmetic Progression:

It is a series in which the difference between thw consecutive terms is constant and the difference is called common difference.

Let the terms be a, a+d, a+2d,a+3d,a+4d,.........+(a+nd)

Difference between the consecutive terms = a+d-a=a+2d-(a+d)

                                                                        =d

nth term = a+(n-1)d

               =Sn-Sn-1

    T₄       = S₄-S₃

               =20-12

               =8

Hence the fourth term of AP is 8.