Find the 56 th term of the arithmetic sequence -14,-26,-38,dots Answer:

Identify First Term: To find the 56th term of an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence, which is a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference between the terms.Find Common Difference: First, we identify the first term (a_1) of the sequence, which is -14.Calculate 56th Term: Next, we need to find the common difference (d). We can do this by subtracting the first term from the second term: -26 - (-14) = -26 + 14 = -12.Substitute Values: Now that we have the first term and the common difference, we can find the 56th term (a_56) using the formula: a_56 = a_1 + (56 - 1)d.Perform Calculation: Substitute the known values into the formula: a_56 = -14 + (56 - 1)(-12).Multiply and Add: Perform the calculation inside the parentheses first: 56 - 1 = 55.Now multiply 55 by the common difference, -12: 55 * -12 = -660.Finally, add the first term to this product to find the 56th term: a_56 = -14 + (-660) = -674.

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Find the 56 th term of the arithmetic sequence
-14,-26,-38,dots
Answer:

Find the $56$ th term of the arithmetic sequence $-14,-26,-38, \ldots$ $\newline$ Answer:

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Q. Find the

56

th term of the arithmetic sequence

-14,-26,-38, \ldots

\newline

Answer:

Identify First Term: To find the $56^{th}$ term of an arithmetic sequence, we need to 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 between the terms.
Find Common Difference: First, we identify the first term $a_1$ of the sequence, which is $-14$ .
Calculate $56^{th}$ Term: Next, we need to find the common difference $(d)$ . We can do this by subtracting the first term from the second term: $-26 - (-14) = -26 + 14 = -12$ .
Substitute Values: Now that we have the first term and the common difference, we can find the $56^{\text{th}}$ term ( $a_{56}$ ) using the formula: $a_{56} = a_1 + (56 - 1)d$ .
Perform Calculation: Substitute the known values into the formula: $a_{56} = -14 + (56 - 1)(-12)$ .
Multiply and Add: Perform the calculation inside the parentheses first: $56 - 1 = 55$ .
Multiply and Add: Perform the calculation inside the parentheses first: $56 - 1 = 55$ .Now multiply $55$ by the common difference, $-12$ : $55 \times -12 = -660$ .
Multiply and Add: Perform the calculation inside the parentheses first: $56 - 1 = 55$ .Now multiply $55$ by the common difference, $-12$ : $55 \times -12 = -660$ .Finally, add the first term to this product to find the $56$ th term: $a_{56} = -14 + (-660) = -674$ .