1. In a geometric series with first term, a and common ratio, r (where r is real and r#1), the sum of the first 7 terms is 4 times the sum of the following 7 terms. Find the ratio of the sum of the first 21 terms to the sum of the first 14 terms.​

9514 1404 393

  21/20

Step-by-step explanation:

Let Sa, Sb, and Sc represent the sums of the first 7 terms, the next 7 terms, and the 7 terms following that. The problem statement tells us ...

  Sa/Sb = 4/1

We know from the nature of geometric series that this means ...

  Sb/Sc = 4/1

Then the desired ratio is ...

  S21/S14 = (Sa +Sb +Sc)/(Sa +Sb) = (Sa +Sa/4 +(Sa/4)/4)/(Sa +Sa/4)

  = (1 +1/4 +1/16)/(1 +1/4) = (16 +4 +1)/(16 +4) . . . . factor out Sa; multiply by 16/16

  S21/S14 = 21/20

45

step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet