Question

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What is the sum of the first 7 terms of the series −4+8−16+32−... ?

Answer 1

`\text{It's a geometric sequence with:}\\\\a_1=-4\\\\r=8:(-4)=-2`


`\text{The formula of the sum of a geometric sequence is:}\\\\S_n=\dfrc{a_1(1-r^n)}{1-r}`


`\text{substitute:}\\\\n=7;\ a_1=-4;\ r=-2\\\\S_7= (-4(1-(-2)^7))/(1-(-2))=(-4(1+128))/(1+2)=(-4\cdot129)/(3)=-172`