Q. 8 A4.0( 4 Votes )

Find the 6th term from end of the A.P. 17, 14, 11,… – 40.

Answer :

Here, a = 17, d = 14 – 17 = –3 and l = –40


where l = a + (n – 1)d


Now, to find the 6th term from the end, we will find the total number of terms in the AP.


So, –40 = 17 + (n – 1)(–3)


–40 = 17 –3n + 3


–40 = 20 – 3n


–60 = –3n


n = 20


So, there are 20 terms in the given AP.


Last term = 20th


Second last term = 20 – 1 = 19th


Third last term = 20 – 2 = 18th


And so, on


So, the 6th term from the end = 20 – 5 = 15th term


So, an = a + (n – 1)d


a15 = 17 + (15 – 1)(–3)


a15 = 17 + 14 × –3


a15 = 17 – 42


a15 = –25


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