136k views
2 votes
Write an explicit formula for a^n the nth term of the sequence 1,3,9....

(instead of the ^ it’s faced down if yk what i mean) please help i’m struggling thank you

1 Answer

2 votes

Answer:

a_n = 3^(n -1)

Explanation:

The n-th term of a geometric sequence with first term a1 and common ratio r is given by ...

a_n = a1·r^(n-1)

Your sequence has first term 1 and ratio r=3, so the sequence is given by ...

a_n = 3^(n -1)

_____

Comment on sequences and series

The sequences we commonly study are "arithmetic" and "geometric." Each of these has an explicit formula for the n-th term, based on the first term and the common difference or ratio. Similarly, each series (sum of terms of a sequence) also has a formula. That's 4 formulas to keep track of; not difficult. One of them, the formula for the n-th term of a geometric sequence, is shown above.

User Mlathe
by
7.9k points