Another arithmetic sum series

radnorgardens

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Question: The first term of an arithmetic series is 16 (a). The 30th term (n) is 100. Calculate S30.

So again, I have the formula:
Sn=n/2[2(a)+(n-1)d].

Using the data above:
S30=30/2[2(16)+(30-1)d]
S30=30/2[32+29d]

Again, I don't understand my next step, or maybe my initial steps are completely wrong. I don't know what to do with the '100', nor 'd' (the common difference). Another attempt:

1st term = 16
30th term = 100

Stuck!

Thanks for any pointers.
 
Question: The first term of an arithmetic series is 16 (a). The 30th term (n) is 100. Calculate S30.

So again, I have the formula:
Sn=n/2[2(a)+(n-1)d].

Using the data above:
S30=30/2[2(16)+(30-1)d]
S30=30/2[32+29d]

Again, I don't understand my next step, or maybe my initial steps are completely wrong. I don't know what to do with the '100', nor 'd' (the common difference). Another attempt:

1st term = 16
30th term = 100

Stuck!

Thanks for any pointers.

The equation can be re-written as:

Sn= n/2 * [a1 + an]

you are given a1 =16 & a30 = 100 → solve for S30
 
Something's wrong with that. Check the original problem.
1st term should be 13 OR 100 is the 29th term.
As is, d = 84/29

That is no-doubt a "funky" d - improbable but not impossible.

I believe the objective of the problem was to use the equation I posted - the author probably did not check for value of 'd'.
 
Attached..

6. The first term of an arithmetic series is 16. The thirtieth term is 100. Calculate S30.
Didn't they give you a formula for the sum, Sn, of the first n terms of a sequence, given the first term a1 and the n-th term an? Why not just plug into that? ;)
 
Thank you, but to understand the formula?

S30 = 30/2 * [a1 + an]
S30 = 15 * [116]
S30 = 1740

Great - thanks, that tallies up with the answer key, but how do you get from:
Sn= n/2 * [2(a)+(n-1)d]
to
Sn= n/2 * [a1 + an] ?
 
....how do you get from:
Sn= n/2 * [2(a)+(n-1)d]
to
Sn= n/2 * [a1 + an] ?
Well, a = a1, right? And what is the formula for an, in terms of a = a1, n, and d? When you plug that all in to the second formula, what do you get when you simplify down? ;)
 
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