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Consider the arithmetic series:

1 + 9 + 17 + 25 + ...

Write a formula for the sum of the first n terms in this series.
A) 4n2 - 3n
B) 6n2 - 7n
C) 8n2 - 5n
D) 10n2 - n

Respuesta :

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1st nth sum is given by:

n ----   Sum                           Expression

1 ----    1                           --- 4*1^2 -3*1

2 ----    1+9 = 10               --- 4*2^2 -3*2

3 ----    1+9+17 = 27         --- 4*3^2 -3*3

4 ----    1+9+17+25 = 52   --- 4*4^2 -3*4

Therefore, the best expressions is;

Sum of 1st nth terms = 4n^2 - 3n

Then,

The correct answer is A.

Answer: A) 4n² - 3n

Step-by-step explanation:

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

Looking at the given sequence,

a = 1

d = 9 - 1 = 17 - 9 = 8

Therefore, the formula for the sum of the first n terms in this series would be

Sn = n/2[2 × 1 + (n - 1)8]

Sn = n/2[2 + 8n - 8]

Sn = n/2[ 8n - 8 + 2]

Sn = n/2[ 8n - 6]

Sn = 4n² - 3n

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