Terms and sequence

Question

The diagrams are made up of hexagons.

Diagram 1 = 6 hexagons

Diagram 2 = 10 hexagons

Diagram 3 = 14 hexagons

Diagram 4= 18 hexagons

b) Find an expression, in terms of n, for the nth term of the series.

c) Is it possible to have a diagram with 356 hexagons? Briefly explain your answer.

Answer 1

AN= A1+ (N-1)d where A1=6 and d= common difference = 4

AN=6+(N-1)(4) = 6+4N-4 = 4N+2

AN = 4N+2

4N+2 = 356

4N = 354

N = 354/4 = 88 1/2

since N is always an integer, 356 cannot be a term in the sequence

356 is, 352 is, but not 354