Question

1 4 a) Is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.

Answer 1

THe length of each cube is inreasing by 1. This means that the increment is in arithmetic sequence.

The formula for determining the nth term of an aritmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first tem of the sequence

Common difference, d represents the difference between consecutive terms

Given that a = 3, d = 1

Tn = 2 + (n - 1)1

Tn = 2 + n - 1

Tn = 1 + n

For the 18th term, n = 18

T18 = 1 + 18 = 19

The number of boxes in the square for the 19th term is

19 * 19 = 361