Question

the next term of A.P(a+3d),(a+d),(a-d)...

Answer 1

Given:

Arithmetic progression is given as  (a+3d),(a+d),(a-d)

To Find:

Find the next term T₄

Solution:

given progression is (a+3d),(a+d),(a-d),

As in the arithmetic progression, difference between the consecutive terms is constant which is known as common ratio.

T₁= (a+3d)

T₂=(a+d)

T₃=(a-d),

By the definition of AP

T₄-T₃=T₃-T₂

T₄=2T₃-T₂

  =2(a-d)-(a+d)

  =2a-2d-a-d

  =a-3d

Hence the fourth term of the AP is (a-3d).

Answer 2

Given: AP series   $(a + 3d), (a + d), (a - d)......$

Since we know that the common difference is

                     $(a+d) - (a+3d) = -2d$

then the fourth term in the series will be

                   $(a-d)+(-2d)= (a-3d)$

so the next term will be $(a-3d)$

#SPJ2