Question

Find these terms of the sequence (An}, where An = 2(3)n + 5

Answer 1

Given the sequence A_n , the terms of the sequence can be found by substituting for values of n, where n=1,2,3,4,5,6,7,8, ... in the general term of that sequence.

Given A_n= 2(3)n + 5 the terms of this sequence are given by,

A₁=2(3)1+5=6+5=11

A₂=2(3)2+5=12+5=17

A₃=2(3)3+5=18+5=23

A₄=2(3)4+5=24+5=29

A₅=2(3)5+5=30+5=35

A₆=2(3)6+5=36+5=41

A₇=2(3)7+5=42+5=47

A₈=2(3)8+5=48+5=53

A₉=2(3)9+5=54+5=59

A₁₀=2(3)10+5=60+5=65

This procedure is continued until the desired number of terms of the sequence are found

Therefore, the first ten terms of this sequence are,

11,17, 23,29,35,41,47,53,59,65, ...