Question

Find the 20th term from the end for the A.P.: 2,5,8,…….251.​

Answer 1

common difference = 5-2=3

Writing this A.P. in reverse order

251,248,245,…,8,5,2

Now, for the new A.P., we have

a=251

d=248−251

d= -3

We want to find 20th term, so n=20

By using nth term t

n

=a+(n−1)d we have

a20 = a + 19d

= 251 + 19×-3

= 194

20th term from the end is 194

Answer 2

$a = 2 \\ d = 3 \\ a {}^{20} = a + 19d \\ =2 + 19d \\ = 2 + 19 |3| \\ = 2 + 57 \\ {a}^{20} = 59 \\ 20 {}^{th} term \: of \: n \: ap \: is = 59$