Question
The beginning of an arithmetic sequence is shown below. What is the n^th term rule for this sequence?
Answer
4.2
(284 Votes)
Kian
Professional · Tutor for 6 years
Answer
The sequence
looks like the sequence
except that each term is multiplied by 2 and an additional 3 is added. So, the expression that describes this sequence is
, where
represents the position of a term in the sequence. Let's verify the first four terms:1. To find the
term, plug in
:
2. To find the
term, plug in
:
3. To find the
term, plug in
:
4. To find the
term, plug in
.
Considering the explicit second-order difference and inspections for the terms, it is obvious that the sequence
can be described by the rule
.