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Find the $$20^{th}$$ term from the last term of the AP: 3, 8, 13… , 253.

We want to find $$20^{th}$$ term from the last term of given AP.

So, let us write given AP in this way:253 … 13, 8, 3
Here First term = a = 253,
Common Difference = d
= 8 – 13 = –5

Using formula $$a_n = a + (n - 1)d$$, to find $$n^{th}$$ term of arithmetic progression,

= 253 + (20 - 1) (-5)
= 253 + 19 (-5)
= 253 – 95
= 158

Therefore, the $$20^{th}$$ term from the last term of given AP is 158.