# Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253

To find: 20th term from the last

In the given AP
First term,a = 3
common difference, d = 5
we know, nth term of an AP is
an = a + (n - 1)d

Now, Let the no of terms in given AP is n
last term = 253

⇒ 253 = a + (n - 1) d

253 = 3 + (n -1) x 5

253 = 3 + 5n – 5 = – 2

5n = 253 + 2 = 255

n = 255/5 = 51

Total number of terms in AP is 51

If there are n terms in an AP then some mth term from end will be equal to n - m + 1 term from beginning

Therefore, 20th term from the last term will be 32th term from starting (as, 51 - 20 + 1 = 32)

a32 = a + 31d

= 3 + 31 x 5

= 3 + 155 = 158

Thus, required term is 158

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