Find the sum of the first 10 terms of the arithmetic series.

Question

-5+0+5+10+....

 

Answer 1

Hello Dhelmalyz!

 

To solve this, we need to know a few things. First, let's figure out what the equation is for the arithmetic sequence.

a₁ is -5

and d= +5

 

**recall that the formula for an arithmetic sequence is a_n=a₁+d(n-1)

 

for the summation, we know that we're starting with k=1, and ending at n=10. The summation will look like this...

 

10

Σ 5n-10

k=1

 

To find the sum, we can use the equation n(a₁+a₁₀)/2----to find a₁ and a₁₀, we plug in 1 and 10 into our equation

 

10(-5+40)/2

 

10(35)/2

350/2

175

 

The total sum is 175. If you want to check your answer, add 5 to each term and add the first 10 together. 

-5+0+5+10+15+20+25+30+35+40=175

 

Hope that helps!

Nikita