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Find the 1 oth term of the arithmetic sequence
-2x-3,4x+3,10 x+9,dots
Answer:

Find the $1$ oth term of the arithmetic sequence $-2 x-3,4 x+3,10 x+9, \ldots$ $\newline$ Answer:

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Solve exponential equations using natural logarithms

Full solution

Q. Find the

1

oth term of the arithmetic sequence

-2 x-3,4 x+3,10 x+9, \ldots

\newline

Answer:

Identify first term: To find the $10^{th}$ term of an arithmetic sequence, we need to determine the common difference and use the formula for the $n^{th}$ term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ , where $a_n$ is the $n^{th}$ term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
Find common difference: First, let's identify the first term $a_1$ of the sequence. The first term given is $-2x-3$ .
Calculate $10$ th term: Next, we need to find the common difference $d$ . The common difference is the difference between any two consecutive terms. We can find it by subtracting the first term from the second term: $(4x+3) - (-2x-3) = 4x + 3 + 2x + 3 = 6x + 6$ .
Substitute values: Now that we have the first term and the common difference, we can find the $10$ th term ( $a_{10}$ ) using the formula: $a_{10} = a_1 + (10 - 1)d$ .
Simplify equation: Substitute the values into the formula: $a_{10} = (-2x-3) + (10 - 1)(6x + 6)$ .
Combine like terms: Simplify the equation: $a_{10} = -2x - 3 + 9(6x + 6) = -2x - 3 + 54x + 54$ .
Final result: Combine like terms: $a_{10} = -2x + 54x - 3 + 54 = 52x + 51$ .
Final result: Combine like terms: $a_{10} = -2x + 54x - 3 + 54 = 52x + 51$ .The $10$ th term of the arithmetic sequence is $52x + 51$ .

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