Can anyone help me with this, don't know where to start.

[dreamlover]

Here is an arithmetic sequence:

index (n)	1	2	3	4	5	6	7	8
term (an)	10	22	34	46	58	70	82	94

Pick method (1) or (2) to find the partial sum of the first 100 terms for this sequence.

1. Use the explicit formula, an = a₁ + (n-1) d to find the 100th term for this sequence. Then use the partial sum formula sn = n/2 (a₁ + an) formula to find s100.
2. Use technology (https://www.desmos.com/calculator) to find s100 using sigma notation with the explicit formula.

100
∑ (a₁ +(n−1)d)
n=1
Explain which method you used, show or explain what you did.

 

[Otis]

... Explain which method you used, show or explain what you did.

Are you instructing us to complete the exercise for you?

Wait ... don't answer that. Read the forum's submission guidelines, instead, and then show your work (or explain why you're stuck). Thank you!

 

[pka]

Here is an arithmetic sequence:

index (n)	1	2	3	4	5	6	7	8
term (an)	10	22	34	46	58	70	82	94

Pick method (1) or (2) to find the partial sum of the first 100 terms for this sequence.
1. Use the explicit formula, an = a₁ + (n-1) d to find the 100th term for this sequence. Then use the partial sum formula sn = n/2 (a₁ + an) formula to find s100.
2. Use technology (https://www.desmos.com/calculator) to find s100 using sigma notation with the explicit formula.
100
∑ (a₁ +(n−1)d)
n=1

One of the most widely used sum is the Gauss sum \(\displaystyle \sum\limits_{k = 1}^N k = \frac{{N(N + 1)}}{2}\), that is the sum of the first N positive integers.
A quick glance at the question reveals that \(\displaystyle a_1=10~\&~a_n=a_1+(n-1)\cdot 12\)
\(\displaystyle \begin{align*}\sum\limits_{k = 1}^{100} {\left( {10 + (k - 1) \cdot 12} \right)} &= \sum\limits_{k = 1}^{100} {(10)} + \sum\limits_{k = 1}^{100} {(k - 1)(12)} \\& = \sum\limits_{k = 1}^{100} {(10)} + (12)\sum\limits_{k = 1}^{99} {(k)} \\& = 100(10) + (12)\frac{{(99)(100)}}{2}\end{align*}\)
Can you finish by giving reasons for those steps?