Determine the number of terms, n, given the geometric series -1 - 2 - 4 - 8 - ... and Sn=−31.

5

Step-by-step explanation:

We are given the geometric series:

-1, - 2, - 4, - 8

In the geometric series above, the common ratio = second term/first term = -2/-1

= 2

Where common ratio is greater than 1(r >1)

The sum of a geometric progression =

Sn = a(rⁿ -1)/r - 1

In the question we are asked to find the number of term = n

Sn = -31

a = -1

r = 2

Hence,

-31 = -1(2ⁿ - 1)/2 - 1

-31 = -1(2ⁿ - 1)

-31 = -2ⁿ + 1

2ⁿ = 1 + 31

2ⁿ = 32

2ⁿ = 2^5

n = 5

Therefore, the number of terms(n) = 5

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .