Question

here are the first four of an arithmetic sequence.

6 10 14 18
(a) Write an expression , in terms of n, for the nth term of this sequence

The nth term of a different arithmetic sequence in 3n + 5

(b) is 108 a term of this sequence? show how you you get your answer.

Answer 1

a)
6, 10, 14, 18

a = 6 = first term.

common difference, d = 10 - 6 = 4

nth term of an arithmetic sequence = a + (n - 1)*d = 6 + (n - 1)4

= 6 + 4*n - 4*1

= 4n - 4 + 6

= 4n + 2

nth term of the arithmetic sequence is 4n + 2

b)
different arithmetic = 3n + 5

If 108 is on the sequence, it would have a whole number solution for n.

3n + 5 = 108

3n = 108 - 5

3n = 103

n = 103/3 = 34 1/3

n is not a whole number, so 108 is not a term of the sequence.

Hope this helps.