Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

What is the sum of the first 19 terms of the arithmetic series?

3+8+13+18+…

Answer 1

Answer: 912

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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

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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.

Answer 2

Answer: 912

Explanation:

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

• the first term (a₁) = 3
• the difference (d) = 5

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

`a_n=a_1+d(n-1)\\.\quad =3+5(n-1)\\.\quad =3+5n-5\\.\quad =5n-2`

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

`a_n=5n-2\\a_(19)=5(19)-2\\.\quad =95-2\\.\quad =93`

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

`S_n=(a_1+a_n)/(2)* n\\\\S_(19)=(a_1+a_(19))/(2)* 19\\\\.\quad =(3+93)/(2)* 19\\\\.\quad =(96)/(2)* 19\\\\.\quad =48* 19\\\\.\quad =912`