Question

For the arithmetic sequence beginning with the terms {-2, 0, 2, 4, 6, 8...}, what is the sum of the first 18 terms?

Answer 1

given,n=18

a=-2

so, we can find d (coming difference)=0-(-2) = 2

s(18)=n/2 (2a+(n-1)d

=18/2 (2*-2 +(18-1)2

=9*30 = 270

Answer 2

Final Answer:

The sum of the first 18 terms in the arithmetic sequence is 288.

Given:

The given arithmetic sequence begins with the terms {-2, 0, 2, 4, 6, 8...}.

To Find:

The sum of the first 18 terms in the arithmetic sequence.

Explanation:

The following points are essential for this solution.

• In an AP or an Arithmetic Progression, the terms are related to the succeeding ones by the common difference.
• The sum of the n terms in an AP with respect to the common difference d and its first term a is $S_n=\frac{n}{2} [a+(n-1)d]$.

Step 1 of 2

From the stated sequence, write the following values.

• The first term is $a=-2$
• The common difference is

$d\\=0-(-2)\\=2-0\\=4-2\\=2$

Step 2 of 2

In line with the above-calculated parameters, the sum of the first 18 terms is

$S_{n=18}\\=\frac{18}{2} [(-2)+(18-1)\times 2]\\=9\times (-2+17\times 2)\\=9\times(-2+34)\\=9\times 32\\=288$

Therefore, the first 18 terms in the arithmetic sequence sum up to the required value of 288.

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