If the sum of the first 12 of a geometric series is 8190 and the common ratio is 2. Find the first term and the 20th term.

Step-by-step explanation:

Geometric Series

The sum of the first n terms of a geometric series whose first term is a1 and a common ratio r is

The problem provides the following data

Replacing the values in the formula:

Operating

Solving for a1

The first term is 2

The general term of the series is

Compute the 20th term

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47