Question

find the sum of the first 30 terms of the sequence below plz and explain.
A[n]=4[n]+1

Answer 1

Similar Example:

find the sum of the first 18 terms of the sequence
A[n] = 7n + 3



Step 1) Find the first term. To do that, we plug in n = 1

A[n] = 7n + 3
A[1] = 7(1) + 3
A[1] = 10

The first term is a1 = 10


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Step 2) Find the last term being added. In this example, the last term is the 18th term and that happens when n = 18


A[n] = 7n + 3
A[18] = 7(18) + 3
A[18] = 129

The last term being added up is a18 = 129



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Step 3) Now use this formula


\[\Large S_n = \frac{n(a_1 + a_n)}{2}\]

\[\Large S_{18} = \frac{18(a_1 + a_{18})}{2}\]

\[\Large S_{18} = \frac{18(10+129)}{2}\]

\[\Large S_{18} = \frac{18(139)}{2}\]

\[\Large S_{18} = 9(139)\]

\[\Large S_{18} = 1,251\]



So in my example, if you add up the first 18 terms (a1 through a18) for the sequence A[n] = 7n+3, you'll get the result 1251


Keep in mind that this is just an example and not the solution to your specific problem; however, it's very similar to what you have. So hopefully this helps you out. If not, then tell me where you are getting stuck.

Answer 2

ty