Question

Find the 3 geometric means between 32 and 162

Answer 1

Geometric means

32, ax1, ax2, ax3, 162

___________________________

S1 = 32 = a1 r^(n-1)

S5 = 162 = a1 r^ (n-1)

________________

32 = a1 r^0

32= a1

S5 = 162 = a1 r^ (5-1)

S5 = 162 = 32 r^ (4)

162/ 32 = r^ (4)

r= 3/2

____________

Sn = 32 (3/2)^ (n-1)

_____________

n=2

S2 = 32 (3/2)^ (2-1)

S2 = 32 (3/2)^ (1)

S2 = 48

n=3

S3 = 32 (3/2)^ (3-1)

S3 = 32 (3/2)^ (2)

S3 = 32 (9/4)

S3= 72

n=4

S4 = 32 (3/2)^ (4-1)

S4 = 32 (3/2)^ (3)

S4 = 32 (27/8)

S4= 108

__________________

Answer

32, 48, 72, 108, 162