Correct answer only ! what is the sum of the first 19 terms of the arithmetic series? 3+8+13+18+…

912

Work Shown:

The starting term is a1 = 3. The common difference is d = 5 (since we add 5 to each term to get the next term). The nth term formula is

an = a1+d(n-1)

an = 3+5(n-1)

an = 3+5n-5

an = 5n-2

Plug n = 19 into the formula to find the 19th term

an = 5n-2

a19 = 5*19-2

a19 = 95-2

a19 = 93

Add the first and nineteenth terms (a1 = 3 and a19 = 93) to get a1+a19 = 3+93 = 96

Multiply this by n/2 = 19/2 = 9.5 to get the final answer

96*9.5 = 912

I used the formula

Sn = (n/2)*(a1 + an)

where you add the first term (a1) to the nth term (an), then multiply by n/2

As a check, here are the 19 terms listed out and added up. We get 912 like expected.

3+8+13+18   +23+28+33+38    +43+48+53+58    +63+68+73+78   +83+88+93 = 912

There are 19 values being added up in that equation above. I used spaces to help group the values (groups of four; except the last group which is 3 values) so it's a bit more readable.

 912

Step-by-step explanation:

The given sequence {3, 8, 13, 18, ... } provides the following information:

We can use the information above to find the explicit rule of the sequence:

We can use the explicit rule to find the 19th term (a₁₉)

Next, we can input the first and last term of the sequence into the Sum formula:

351.23

step-by-step explanation: