Q. 24.6( 10 Votes )

Find the first five terms of the sequence, defined by

a1 = 1, an = an–1 + 3 for n ≥ 2.

Answer :

To Find: First five terms of a given sequence.


Condition: n ≥ 2


Given: a1 = 1, an = an–1 + 3 for n ≥ 2


Put n= 2 in nth term (i.e. an), we have


a2 = a2–1 + 3 = a1 + 3 = 1 + 3 = 4 (as a1 = 1)


Put n= 3 in nth term (i.e. an), we have


a3 = a3–1 + 3 = a2 + 3 = 4 + 3 = 7 (as a2 = 4)


Put n= 4 in nth term (i.e. an), we have


a4 = a4–1 + 3 = a3 + 3 = 7 + 3 = 10 (as a3 = 7)


Put n= 5 in nth term (i.e. an), we have


a5 = a5–1 + 3 = a4 + 3 = 10 + 3 = 13 (as a2 = 10)


First five terms of a given sequence is 1, 4, 7, 10, 13


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