Write the sum using summation notation, assuming the suggested pattern continues.

-10 - 2 + 6 + 14 + ... + 110

Question

Write the sum using summation notation, assuming the suggested pattern continues.

-10 - 2 + 6 + 14 + ... + 110

oaktree · Answer

So the equation for a finite arithmetic sum is $$S_{n} =\frac{ n }{ 2 }(a_1 + a_n)$$All we need to do is find n. So we have $$a_n = a_1 + (n-1)d$$And since a_1 is -10 and a_n is 110, and d is obviously 8, we have $$n=\frac{ 110-(-10) }{ 8 } + 1$$ Which is 16. So our sum is$$\frac{ 16 }{ 2 }(-10 + 110) = 8(100) = 800$$Good?

ranga · Answer

Write the sum using summation notation:
$$\Large \sum_{n = 1}^{16}(8n - 18)$$

oaktree · Answer

Oh, summation notation. Sorry. That's right.

anonymous · Answer

Wait how did you get all thst

oaktree · Answer

All what?

anonymous · Answer

no what he wrote

ranga · Answer

I was basing my answer on OakTree's calculations above.

oaktree · Answer

I think she means explain where the argument of the summation came from.

ranga · Answer

We need to find the nth term of the arithmetic series.

ranga · Answer

This is an arithmetic series with first term -10 and common difference 8.
The nth term is given by a_n = a_1 + (n-1)d = -10 + (n-1)(8) = -10 + 8n - 8
a_n = 8n - 18.
We need to sum this as n runs from 1 to 16 (16 was determined to be the number of terms in the series by OakTree above).

ranga · Answer

You can factor the 2 out of the summation.