Q. 64.5( 2 Votes )

Determine the number of terms in the A.P. 3, 7, 11, ..., 399. Also, find its 20th term from the end.

Answer :

Here, a = 3, d = 7 – 3 = 4 and l = 399


To find : n and 20th term from the end


We have,


l = a + (n – 1)d


399 = 3 + (n – 1) × 4


399 – 3 = 4n – 4


396 + 4 = 4n


400 = 4n


n = 100


So, there are 100 terms in the given AP


Last term = 100th


Second Last term = 100 – 1 = 99th


Third last term = 100 – 2 = 98th


And so, on


20th term from the end = 100 – 19 = 81st term


The 20th term from the end will be the 81st term.


So, t81 = 3 + (81 – 1)(4)


t81 = 3 + 80 × 4


t81 = 3 + 320


t81 = 323


Hence, the number of terms in the given AP is 100, and the 20th term from the last is 323.


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