Question

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

Answer 1

Given A.P. is \(3, 8, 13, …, 253\)
Common difference for this A.P. is \(5\).
Therefore, this A.P. can be written in reverse order as:
\(253, 248, 243, ..…, 13, 8, 5\)
For this A.P., 
\(a = 253\)
\(d = 248 − 253 = −5\)
\(n = 20\)
\(a_{20 }= a + (20 − 1) d\)
\(a_{20 }= 253 + (19) (−5)\)
\(a_{20} = 253 − 95 a = 158\)

Therefore, \(20^{th}\) term from the last term is \(158\).