What is the sum of the first 7 terms of the sequence $10 \times {(- 2)}^{i - 1}$ $10xx(-2)^(i-1)$ ?

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Answer 1 · 2016-07-02T05:20:00

430

The sum of the first n terms of a geometric series with first term $a_{1}$ $a_1$ and common ratio r is given by:

$n \sum i = 1 = \frac{a_{1} (1 - r^{n})}{1 - r}$ $sum_(i=1)^n = [a_1(1-r^n)]/(1-r)$

In this example, $n = 7, a_{1} = 10$ $n=7, a_1 = 10$ and $r = - 2$ $r=-2$

Hence, $7 \sum i = 1 = \frac{10 \cdot (1 - {(- 2)}^{7})}{1 - (- 2)}$ $sum_(i=1)^7 = (10*(1-(-2)^7))/(1-(-2))$

$= \frac{10 \cdot (1 - (- 128))}{3}$ $= (10*(1-(-128)))/3$

$= \frac{1290}{3} = 430$ $=1290/3 = 430$

What is the sum of the first 7 terms of the sequence 10×(−2)i−110xx(-2)^(i-1) ?