Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Find the common difference for an arithmetic series with
a1=5 and S10 = 320.

Sagot :

aklee18oo

Answer:

6

Step-by-step explanation:

Let [tex]n = a_{10}[/tex]. We know the formula for the sum of an arithmetic sequence is:

[tex]S_{n} = \frac{n(a_{1}+a_{n} )}{2}[/tex]

Where n is the number term you are finding the sum up to, a1 is the first term, and an is the nth term. We can substitute what we have:

[tex]320=\frac{10(5 + n)}{2}[/tex]

[tex]640=10(n+5)\\64=n+5\\n=59[/tex]

The formula to find the nth term of an arithmetic series is:

[tex]a_{n} = a_{1} + (n-1)d[/tex]

Where d is the common difference. Again, we can plug in what we have;

[tex]59 = 5 + 9d\\9d = 54\\d = 6[/tex]

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.