Question

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

Answer 1

Answer:

6

Step-by-step explanation:

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

$S_{n} = \frac{n(a_{1}+a_{n} )}{2}$

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:

$320=\frac{10(5 + n)}{2}$

$640=10(n+5)\\64=n+5\\n=59$

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

$a_{n} = a_{1} + (n-1)d$

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

$59 = 5 + 9d\\9d = 54\\d = 6$