Write an explicit formula for a_(n), the n^("th ") term of the sequence 2,10,50,dots Answer: a_(n)=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence 2, 10, 50, ... has a common ratio between consecutive terms, as each term is 5 times the previous term. Therefore, it is a geometric sequence.Use Explicit Formula: Use the explicit formula for a geometric sequence, an = a1 * r^(n-1), where a1 is the first term and r is the common ratio. For the sequence 2, 10, 50, ..., the first term, a1, is 2 and the common ratio, r, is 5.Substitute Values: Substitute the values of a1 and r into the formula to write an expression to describe the sequence. The expression for the sequence 2, 10, 50, ... is an = 2 * 5^(n-1).

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
2,10,50,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $2,10,50, \ldots$ $\newline$ Answer: $a_{n}=$

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Math Problems

Algebra 2

Write a formula for an arithmetic sequence

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Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

2,10,50, \ldots

\newline

Answer:

a_{n}=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence $2, 10, 50, ext{...}$ has a common ratio between consecutive terms, as each term is $5$ times the previous term. Therefore, it is a geometric sequence.
Use Explicit Formula: Use the explicit formula for a geometric sequence, $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio. For the sequence $2, 10, 50, \ldots$ , the first term, $a_1$ , is $2$ and the common ratio, $r$ , is $5$ .
Substitute Values: Substitute the values of $a_{1}$ and $r$ into the formula to write an expression to describe the sequence. The expression for the sequence $2, 10, 50, \ldots$ is $a_{n} = 2 \times 5^{(n-1)}$ .