Question

Write a recursive formula for

a
n
a
n
​
, the
n
th
n
th
term of the sequence
3
,
−
4
,
−
11
,
.
.
.
3,−4,−11,....

Answer 1

9514 1404 393

Answer:

• a[1] = 3
• a[n] = a[n-1] -7

Explanation:

A recursive formula consists of two parts:

• initialization (rule for the first term(s))
• rule for the next term

When we look at the differences between terms in the sequence 3, -4, -11, ..., we find that they are constant at -7. That is each term can be found from the previous one by subtracting 7. This is our recursive rule. The first term is obviously 3, so the recursive formula is ...

a[1] = 3

a[n] = a[n-1] -7