Find an explicit formula for the geometric sequence -25,-50,-100,-200,dots". " Note: the first term should be d(1). d(n)=

Identify Terms and Ratio: We need to identify the first term (a_1) and the common ratio (r) of the geometric sequence. The first term a_1 is given as -25. To find the common ratio r, we divide the second term by the first term. r = (-50) / (-25) = 2Calculate Common Ratio: Now that we have the first term a_1 and the common ratio r, we can write the explicit formula for the nth term of a geometric sequence, which is: d(n) = a_1 * r^(n-1) Substitute a_1 = -25 and r = 2 into the formula. d(n) = -25 * 2^(n-1)Write Explicit Formula: Let's perform a quick check to ensure that our formula is correct by plugging in n=1 to see if we get the first term of the sequence. d(1) = -25 * 2^(1-1) = -25 * 2^0 = -25 * 1 = -25 This matches the first term of the sequence, so our formula appears to be correct.

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Find an explicit formula for the geometric sequence

-25,-50,-100,-200,dots". "
Note: the first term should be d(1).

d(n)=

Find an explicit formula for the geometric sequence $\newline$ $-25,-50,-100,-200,\dots$ . $\newline$ Note: the first term should be $d(1)$ . $\newline$ $d(n)=$

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Math Problems

Algebra 1

Write variable expressions for arithmetic sequences

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Q. Find an explicit formula for the geometric sequence

\newline

-25,-50,-100,-200,\dots

\newline

Note: the first term should be

d(1)

\newline

d(n)=

Identify Terms and Ratio: We need to identify the first term $a_1$ and the common ratio $r$ of the geometric sequence. $\newline$ The first term $a_1$ is given as $-25$ . $\newline$ To find the common ratio $r$ , we divide the second term by the first term. $\newline$ $r = (-50) / (-25) = 2$
Calculate Common Ratio: Now that we have the first term $a_1$ and the common ratio $r$ , we can write the explicit formula for the $n$ th term of a geometric sequence, which is: $\newline$ $d(n) = a_1 \cdot r^{(n-1)}$ $\newline$ Substitute $a_1 = -25$ and $r = 2$ into the formula. $\newline$ $d(n) = -25 \cdot 2^{(n-1)}$
Write Explicit Formula: Let's perform a quick check to ensure that our formula is correct by plugging in $n=1$ to see if we get the first term of the sequence. $d(1) = -25 \times 2^{(1-1)} = -25 \times 2^0 = -25 \times 1 = -25$ This matches the first term of the sequence, so our formula appears to be correct.