B. The Geometric Mean Between The First Two Terms In A Geometric Sequence Is 32. If The 3rd Term Is 4, Find The First Term

B. The geometric mean between the first two terms in a geometric sequence is 32. If the 3rd term is 4, find the first term

 

Answer:

64

Step-by-step explanation:

B. The geometric mean between the first two terms in a geometric sequence is 32. If the 3rd term is 4, find the first term

Given: Geometric mean (first 2 terms) = 32

           3rd term (a3)= 4

Required: first term

Geometric mean (GM)

GM = nth root of (a1 × a2 × a3 × an)

n = 2

a1 =  1st term

a2 = 2nd term

a2 / a1 = a3 / a2

(a2)² = (a1)(a3)

a2 = √(a1)(a3)

GM = √a1 × √(a1 × a3)

32 = √a1 × √(a1 × 4)

solve for a1

a1 = 64

a2 = √(64 × 4)

a2 = 16

16/64 = 4 /16           ??

1/4 = 1/4                   Therefore it is correct