Given:
and
where
.
To find:
The explicit formula for the given recursive formula.
Solution:
We know that recursive formula of an AP is:
Where, d is the common difference.
We have,
Here, d=9.
The first term of the AP is .
The explicit formula for an AP is:
Substituting and
, we get
Therefore, the required explicit formula for the given sequence is .
We have been given that a geometric sequence's 1st term is equal to 1 and the common ratio is 6. We are asked to find the domain for n.
We know that a geometric sequence is in form , where,
= nth term of sequence,
= 1st term of sequence,
r = Common ratio,
n = Number of terms in a sequence.
Upon substituting our given values in geometric sequence formula, we will get:
Our sequence is defined for all integers such that n is greater than or equal to 1.
Therefore, domain for n is all integers, where .