Question

FIND the 4th term from the end of the A.P. ................ 2 , 5 , 8 ................ , 35

Answer 1

Given,

An A.P = 2, 5, 8..,35

To Find,

4th term from the last.

Solution,

In the given A.P

a = 2

d = 3

Now,

35 = a+(n-1)d

35 = 2+(n-1)3

33 = 3n-3

36 = 3n

n = 12

So, the fourth last term would be 9th term

a+8d = 2+8*3

        = 2+24

        = 26

Hence, the 4th term from the end is 26.

Answer 2

We must recall that:

Arithmetic progression is a progression in which every term after the first is obtained by adding a constant value, called the common difference (d). So, to find the nth term of an arithmetic progression, we know $an=a1+(n-1)d.$

Given,

An A.P $=2,5,8,...,35$

In the given A.P

$a=2\\d=3$

Now,

$35=a+(n-1)d\\35=2+(n-1)3\\33=3n-3\\36=3n\\n=12$

So, the fourth last term would be $9^t^h$ term

$a+8d=2+8\times3\\=2+24\\=26$

Hence, the 4th term from the end is $26.$