Question

For the following sequence, determine if it is an arithmetic sequence, geometric sequence, or neither. If it is either arithmetic or geometric, give the next two terms in the sequence. 2,6,10,14,...

Answer 1

Remark

Each term and the next one is separated by 4.

14 - 10 = 4

6 - 1 = 4

The common difference is 4

d = 4

General equation for this series

t_n = a + (n - 1)*d

t_n =2 + (n-1) * 4

Next 2 terms

t5 = 2 + (5 - 1)*4 substitute 5 for n

t5 = 2 + 4*4 Calculate the answer

t5 = 18

t_6

t6 = 2 + (6 -1)*4

t6 = 2 + 5*4

t6 = 22

I hope you can figure out the last one. Just look up at t5