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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]

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