a sequence is defined as an infinite or finite sequence An i

a sequence is defined as an infinite or finite sequence. An infinite sequence {an } is a function whose domain is the set of positive integers. The function values, or terms, of the sequence are represented by a1, a2, a3, a4, . . . , an , ...

Sequences whose domains consist only of the first n positive integers are called finite sequences.

Given the term an = 3n + 4, how would you express the first four terms of the sequence, and what insight did you gain?

Solution

For 1st term,put n=1
a1 = 3*1+4 = 7

for 2nd term, put n=2
a2 = 3*2+4 = 10

for 3rd term,put n=3
a3 = 3*3+4 = 13

for 4th term,put n=4
a4 = 3*4 + 3 = 17

I came to know that this series is an Arithmetic Profression with 1st element = 7 and common difference = 3