Question

The diagram below represents the first three terms of a sequence. Assuming the pattern continues,which formula determines an, the number of squares in the nth term ?

Answer 1

Answer: 3n+1

Explanation:

Answer 2

The correct answer is B)
`a_n=3n+1`

Writing the sequence numerically, we have 4, 7, 10, ...

This is an arithmetic sequence, since there is a constant, 3, added each time. This gives us the explicit formula

`a_n=4+3(n-1)`

Using the distributive property, we have

`a_n=4+3*n-3*1 \\ \\a_n=4+3n-3`

Combining like terms, we have

`a_n=3n+1`