Question

find the 20th term from the last term of the Ap 3,8,13..........253.

Answer 1

Heya,

A.P. = 3, 8, 13, ....253

Let us inverse the A.P. to get the 20th term from the last,

Now,
A.P. = 253, 248.....8, 3
a = 253
d = 248 - 253
= -5
n = 20

An = a + (n-1)d
A20 = 253 + (20 - 1)(-5)
A20 = 253 - 19×5
A20 = 253 - 95
A20 = 158

So, 20th term from the last is 158.

Hope this helps...:)

Answer 2

a = 3

d = 5

Tn = 253

=> a + (n-1)d = 253

=> 3 + (n-1) 5 = 253

=> (n-1)*5 = 250

=> n-1 = 50

=> n = 51

Total number of terms = 51


20th term from last is 32th term from beginning

T32 = 3 + (32-1) * 5

T32 = 3 + 31 * 5

T32 = 3 + 155

T32 = 158


20th term from last = 158