Find The Sum In The Geometric Series 40+(-20)+10+(-5)+5/2+(-5/4)

Find the sum in the geometric series 40+(-20)+10+(-5)+5/2+(-5/4)

 

Answer:

S₆ = 105/4  

Step-by-step explanation:

Geometric sequence:  40, -20, 10, -5, 5/2, -5/4

Find the common ratio, r:

r = a₂/a₁ = a₃/a₂

r = -20/40 = -5/10

r = -1/2

Sum of geometric series:

Sn = (a₁) (1-rⁿ)/(1-r)

Where:

Sn = sum, unknown

a₁ = first term, 40

r = common ratio, -1/2

n = number of terms, 6

Solution:

S₆ = (40) (1-(-1/2)⁶) / (1 - (-1/2)

S₆ = (40) 1-(1/64) / 1+1/2

S₆ = (40) 64/64 - 1/64 / (3/2)

In dividing fractions,multiply dividends by reciprocal of divisor:

Reciprocal of 3/2 = 2/3

S₆ = (40) (63/64) (2/3)

S₆ = (40)(21/32)

S₆ = (5)(21/4)

S₆ = 105/4