Find the 55^("th ") term of the arithmetic sequence 11,30,49,dots Answer:

Arithmetic Sequence Formula: To find the 55th 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.Determine Common Difference: First, we need to determine the common difference (d) of the sequence. We can do this by subtracting the first term from the second term: d = 30 - 11 = 19.Plug in Values: Now that we have the common difference, we can use the formula to find the 55th term. Let's plug in the values: a_1 = 11 (the first term), n = 55 (since we're looking for the 55th term), and d = 19 (the common difference we found).Calculate 55th Term: Using the formula: a_55 = 11 + (55 - 1) * 19.Perform Calculation: Now, let's do the calculation: a_55 = 11 + 54 * 19.Final Result: Multiplying 54 by 19 gives us 1026. So, a_55 = 11 + 1026.Adding 11 to 1026, we get a_55 = 1037.

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Find the
55^("th ") term of the arithmetic sequence
11,30,49,dots
Answer:

Find the $55^{\text {th }}$ term of the arithmetic sequence $11,30,49, \ldots$ $\newline$ Answer:

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Q. Find the

55^{\text {th }}

term of the arithmetic sequence

11,30,49, \ldots

\newline

Answer:

Arithmetic Sequence Formula: To find the $55^{th}$ 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.
Determine Common Difference: First, we need to determine the common difference $d$ of the sequence. We can do this by subtracting the first term from the second term: $d = 30 - 11 = 19$ .
Plug in Values: Now that we have the common difference, we can use the formula to find the $55^{\text{th}}$ term. Let's plug in the values: $a_1 = 11$ (the first term), $n = 55$ (since we're looking for the $55^{\text{th}}$ term), and $d = 19$ (the common difference we found).
Calculate $55$ th Term: Using the formula: $a_{55} = 11 + (55 - 1) \times 19$ .
Perform Calculation: Now, let's do the calculation: $a_{55} = 11 + 54 \times 19$ .
Final Result: Multiplying $54$ by $19$ gives us $1026$ . So, $a_{55} = 11 + 1026$ .
Final Result: Multiplying $54$ by $19$ gives us $1026$ . So, $a_{55} = 11 + 1026$ . Adding $11$ to $1026$ , we get $a_{55} = 1037$ .