Question

Add the first 9 terms of this sequence:
-7, -7/2, -7/4, -7/8, -7/16, ...

Answer 1

Sum is -3577/256

Explanation:

This is a geometric progression:

`S = \frac{a( 1 - {r}^(n) )}{1 - r } \\ for \: \: r < 1`

S is the sum

a is the first term, a = -7

r is the common ratio, r = -7/2 ÷ -7 = ½

substitute:

`S = \frac{ - 7(1 - {( (1)/(2)) }^(9) }{1 - (1)/(2) } \\ \\ S = ( - 6.986)/( (1)/(2) ) \\ \\ S = - (3577)/(256)`