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Find the
5^("th ") term of the arithmetic sequence
x+3,5x+5,9x+7,dots
Answer:

Find the $5^{\text {th }}$ term of the arithmetic sequence $x+3,5 x+5,9 x+7, \ldots$ $\newline$ Answer:

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Find trigonometric functions using a calculator

Full solution

Q. Find the

5^{\text {th }}

term of the arithmetic sequence

x+3,5 x+5,9 x+7, \ldots

\newline

Answer:

Determine Common Difference: To find the $5^{\text{th}}$ term of an arithmetic sequence, we need to determine the common difference between consecutive terms. $\newline$ Let's find the difference between the second and the first term. $\newline$ Difference = $(5x + 5) - (x + 3)$
Calculate Difference: Now, let's calculate the difference. $\newline$ Difference = $5x + 5 - x - 3$ $\newline$ Difference = $4x + 2$ $\newline$ This is the common difference of the arithmetic sequence.
Find $5$ th Term Formula: To find the $5^{th}$ term, we need to add the common difference to the previous term three more times (since we already have the first two terms). $\newline$ The $n^{th}$ term of an arithmetic sequence can be found using the formula: $\newline$ $n^{th}$ term = first term + $(n - 1) \times$ common difference $\newline$ Let's apply this formula to find the $5^{th}$ term.
Substitute Values: Substitute the known values into the formula. $\newline$ $5^{\text{th}}$ term $= (x + 3) + (5 - 1) \times (4x + 2)$ $\newline$ $5^{\text{th}}$ term $= (x + 3) + 4 \times (4x + 2)$
Perform Multiplication and Addition: Now, let's perform the multiplication and addition to find the $5^{\text{th}}$ term. $5^{\text{th}} \text{ term} = x + 3 + 16x + 8$ $5^{\text{th}} \text{ term} = 17x + 11$ This is the $5^{\text{th}}$ term of the arithmetic sequence.

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