Find the 99th term of the arithmetic sequence -4,7,18,dots Answer:

Identify First Term and Common Difference: To find the 99th term of an arithmetic sequence, we need to know the first term (a1) and the common difference (d). The first term is given as -4.Calculate Common Difference: The common difference (d) can be found by subtracting the first term from the second term. So, d = 7 - (-4) = 7 + 4 = 11.Apply Formula for nth Term: Now that we have the common difference, we can use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d. We want to find the 99th term, so n = 99.Substitute Values and Calculate: Substitute the known values into the formula to find a99. a99 = -4 + (99 - 1) * 11 = -4 + 98 * 11.Perform Multiplication: Perform the multiplication: 98 * 11 = 1078.Perform Addition: Now, perform the addition: a99 = -4 + 1078 = 1074.

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Find the 99th term of the arithmetic sequence
-4,7,18,dots
Answer:

Find the $99$ th term of the arithmetic sequence $-4,7,18, \ldots$ $\newline$ Answer:

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Math Problems

Algebra 1

Evaluate variable expressions for number sequences

Full solution

Q. Find the

99

th term of the arithmetic sequence

-4,7,18, \ldots

\newline

Answer:

Identify First Term and Common Difference: To find the $99^{\text{th}}$ term of an arithmetic sequence, we need to know the first term ( $a_1$ ) and the common difference ( $d$ ). The first term is given as $-4$ .
Calculate Common Difference: The common difference $d$ can be found by subtracting the first term from the second term. So, $d = 7 - (-4) = 7 + 4 = 11$ .
Apply Formula for nth Term: Now that we have the common difference, we can use the formula for the nth term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ . We want to find the $99^{\text{th}}$ term, so $n = 99$ .
Substitute Values and Calculate: Substitute the known values into the formula to find $a_{99}$ . $a_{99} = -4 + (99 - 1) \times 11 = -4 + 98 \times 11$ .
Perform Multiplication: Perform the multiplication: $98 \times 11 = 1078$ .
Perform Addition: Now, perform the addition: $a_{99} = -4 + 1078 = 1074$ .