An AP 5, 8, 11…has 40 terms. Find the last term. Also find the sum of the last 10 terms.


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First Term of the AP (a) = 5

Common difference (d) = 8 - 5 = 3

Last term = a40 = a + (40 - 1) d

= 5 + 39 × 3 = 122

Also a31 = a + 30d = 5 + 30 × 3 = 95

Sum of last 10 terms = \(\frac{n}{2}\)(a31 + a40)

\(\frac{10}{2}\)(95 + 122)

= 5 × 217 = 1085