Find the indicated term of each arithmetic sequence. (B) a n = 5 2 + 3 ( n − 1 ) 4 a_{n}=\frac52+\frac{3\left(n-1\right)}{4} Find a 6 a_6 .

we're asked to find the indicated term of the arithmetic sequence a sub n equals five halves plus three times n minus one over four. And we're told here that we want to find a sub six, our sixth term, which we can do by just plugging six in for n. So to get a sub six, we take five halves plus three times six minus one over four. And then we just need to simplify. So keeping that five halves the same for now, I have three times six minus one. Six minus one is five. So three times five is gonna give us 15. So this is five halves plus 15 fourths. I can give these a common denominator of four by just multiplying this five halves by two over two. That gives us 10 fourths. So 10 fourths plus 15 fourths, just adding those numerators, gives me here 25 over four for that sixth term having just plugged in six for n. Let us know if you have any questions and I'll see you in the next one.

13. Sequences, Series, and the Binomial Theorem

Arithmetic Sequences

Intermediate Algebra

13. Sequences, Series, and the Binomial Theorem

Arithmetic Sequences

Struggling with Intermediate Algebra?

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Multiple Choice

Find the indicated term of each arithmetic sequence.
(B) $a_{n} = \frac{5}{2} + \frac{3 (n - 1)}{4}$
Find $a sub 6$ .

$\frac{25}{4}$

$5$

$10$

$\frac{25}{2}$

Verified step by step guidance

Identify the general form of an arithmetic sequence, which is given by the formula: $a_n = a_1 + (n - 1)d$, where $a_n$ is the nth term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number.

Determine the first term $a_1$ of the sequence. This is usually given or can be found from the problem statement.

Find the common difference $d$ by subtracting the first term from the second term, i.e., $d = a_2 - a_1$.

Use the formula $a_n = a_1 + (n - 1)d$ to express the nth term of the sequence, substituting the values of $a_1$ and $d$.

If the problem asks for a specific term or the sum of terms, plug in the value of $n$ into the formula or use the sum formula for arithmetic sequences: $S_n = \frac{n}{2} (2a_1 + (n - 1)d)$.

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Struggling with Intermediate Algebra?

Find the indicated term of each arithmetic sequence.(B) an=52+3(n−1)4a_{n}=\frac52+\frac{3\left(n-1\right)}{4}Find a6a_6.

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Find the indicated term of each arithmetic sequence.
(B) $a_{n} = \frac{5}{2} + \frac{3 (n - 1)}{4}$
Find $a sub 6$ .