1.) What is the formula for the nth term of the arithmetic sequence that has a common difference of 8 and a first term of 4?
2.) What is the formula for the nth term of the geometric sequence that has a first term of 2 and a ratio of 3?
surely you have those in your text or notes.
first one:
term(n) = a + (n-1)d
and you know both a and d
term(n) = 4 + (n-1)(8)
= 4 + 8n - 8
= 8n - 4
for the second, go to your text, find the formula for
term(n) of a GS , and plug in your given values
9121518
1.) To find the formula for the nth term of an arithmetic sequence, we can use the general formula:
an = a1 + (n - 1)d
where an represents the nth term, a1 is the first term, n is the term number, and d is the common difference.
In this case, the first term is 4 and the common difference is 8. Thus, the formula for the nth term of the arithmetic sequence is:
an = 4 + (n - 1) * 8
2.) To find the formula for the nth term of a geometric sequence, we can use the general formula:
an = a1 * r^(n - 1)
where an represents the nth term, a1 is the first term, n is the term number, and r is the common ratio.
In this case, the first term is 2 and the common ratio is 3. Thus, the formula for the nth term of the geometric sequence is:
an = 2 * 3^(n - 1)