Sequence and terms

Question

Figure 1= 1 square

Figure 1= 4 square

Figure 1= 7 square

Figure 1= 10 square

1. Write down the formula of n for the number of squares in figure n.
2. Explain whether it is possible for a figure to have 90 squares in this sequence.

Answer 1

AN = A1 +(N-1)d where A1 = 1 and d= 3

AN=1 +3(N-1) = 1+ 3N-3 = 3N-2

AN= 3N-2

3N-2 =90

3N = 92

N =92/3 = 30 2/3

since N is an integer 90 is not a term in the sequence. 91 is, 88 is, but not 90

1,4,7,10,13, .3n-2, ..88,91,94, ...