Question

The sum of an arithmetic series where t1 = -2, t3 = 7, and n = 15 is

Answer 1

The sum of the arithmetic series with the parameters  t1 = -2, t3 = 7, and n = 15 is 442.5

How to determine the sum of the series?

The given parameters are:

t1 = -2

t3 = 7

n = 15

Start by calculating the common difference using:

Tn = t1 + (n- 1)d

So, we have:

7 = -2 + (3 - 1) * d

Evaluate

7 = -2 + 2d

Add 2 to both sides

2d = 9

Divide by 2

d = 4.5

The sum  is then calculated using:

$S_n = \frac n2 * (2a + (n - 1) * d)$

So, we have:

$S_{15} = \frac {15}2 * (2*-2 + (15 - 1) * 4.5)$

Evaluate

$S_{15} = 442.5$

Hence, the sum of the arithmetic series is 442.5

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