Question

Which of the following formulas may be used to generate the sequence, 12, 19, 26, 33, 40, …?

A. an = 7n + 5
B. an = n + 7
C. an = 7n + 12
D. an = 2n - 5

Answer 1

We first note that the difference of each 2 consecutive terms is 7:

19-12=7
26-19=7
33-26=7
40-7=7

Let
`\displaystyle{ a_n` represent the n'th term of the sequence,

then clearly:


`\displaystyle{ a_1=7\cdot1+5=12`


`\displaystyle{ a_1=7\cdot2+5=19`


`\displaystyle{ a_1=7\cdot3+5=26`
...
...

Thus,
`\displaystyle{ a_n=7n+5`


Answer: A