the sum of the first n terms of an arithmetic series is Sn=2n^2+5n.

Determine the first 3 terms. Help!!!

I need help for proving the n term

how about calculate the S8?

From which textbook is this question from?

Can you tell me the author please

Oh, I see you're struggling with arithmetic series! Don't worry, I'm here to help... with a little humor, of course!

To find the first three terms, we need to plug in the values of n and see what happens. Ready? Let's clown around with this!

If we start with n = 1, then we substitute it into the formula:
S1 = 2(1)^2 + 5(1)
= 2 + 5
= 7

So, the sum of the first term is 7. Ta-da!

Now, let's move on to n = 2. Substituting into the formula again, we get:
S2 = 2(2)^2 + 5(2)
= 2(4) + 10
= 8 + 10
= 18

And voila! The sum of the first two terms is 18. Clown-firmed!

Lastly, for n = 3. Let's replace n with this value and see what happens:
S3 = 2(3)^2 + 5(3)
= 2(9) + 15
= 18 + 15
= 33

And there you have it! The sum of the first three terms is 33. Clowncluded!

Hope that brought a smile to your face while solving your problem. If you have any more questions or need further assistance, feel free to ask!

To determine the first 3 terms of an arithmetic series, we need to find the values when we plug in n=1, n=2, and n=3 into the formula for the sum of the first n terms (Sn = 2n^2 + 5n).

1. Plug in n=1:
S1 = 2(1)^2 + 5(1)
S1 = 2(1) + 5
S1 = 2 + 5
S1 = 7

So, the sum of the first term is 7.

2. Plug in n=2:
S2 = 2(2)^2 + 5(2)
S2 = 2(4) + 5(2)
S2 = 8 + 10
S2 = 18

So, the sum of the first two terms is 18.

3. Plug in n=3:
S3 = 2(3)^2 + 5(3)
S3 = 2(9) + 5(3)
S3 = 18 + 15
S3 = 33

So, the sum of the first three terms is 33.

Thus, the first three terms of the arithmetic series are 7, 18, and 33.

S1 would be the first term

S1 = 2+5 = 7 , so a = 7
S2 = 2(4) + 10 = 18

S2 = a + a+d = 18
14+d = 18
d = 4

the sequence is: 7, 11, 15, ...

check:
sum3 by formula = 2(9) + 15 = 33
by just adding the 3 terms
= 7+11+15 = 33
All seems good