Write the geometric sequence that has five geometric means between 1and 15,625.

Question

I got:


1, 5, 25, 125, 625, 3,125, 15,625, …

is it ok?

Answer 1

you are correct if your last numbers are 3125 and 15625.

Answer 2

Partially correct.

Let's the first term in the sequence the 1,

So

a1 = 1

If the ratio between terms is r, then any term in the sequence is :

an = a1 ⋅ r ⁿ⁻¹

If there are 5 geometric means between 1 and 15 625, then 15 625 must be the 7th term ( a7 ).

a7 = 1 ⋅ r⁷⁻¹

15 625 = r⁶

r = ⁶√ 15 625

r = ± 5

a1 = 1

r = 5

a1 = 1 ∙ 5⁰ = 1 ∙ 1 = 1

a2 = 1 ∙ 5¹ = 1 ∙ 5 = 5

a3 = 1 ∙ 5² = 1 ∙ 25 = 25

a4 = 1 ∙ 5³ = 1 ∙ 125 = 125

a5 = 1 ∙ 5⁴ = 1 ∙ 625 = 625

a6 = 1 ∙ 5⁵ = 1 ∙ 3 125 = 3 125

a7 = 1 ∙ 5⁶ = 1 ∙ 15 625 = 15 625

1 , 5 , 25 , 125 , 625 , 3 125 , 15 625

and

a1 = 1

r = - 5

a1 = 1 ∙ ( - 5 )⁰ = 1 ∙ 1 = 1

a2 = 1 ∙ ( - 5 )¹ = 1 ∙ ( - 5 ) = - 5

a3 = 1 ∙ ( - 5 )² = 1 ∙ 25 = 25

a4 = 1 ∙ ( - 5 )³ = 1 ∙ ( -125 ) = - 125

a5 = 1 ∙ ( - 5 )⁴ = 1 ∙ 625 = 625

a6 = 1 ∙ ( - 5 )⁵ = 1 ∙ ( - 3 125 ) = - 3 125

a7 = 1 ∙ ( - 5 )⁶ = 1 ∙ 15 625 = 15 625

1 , - 5 , 25 , - 125 , 625 , - 3125 , 15 625

Answer 3

find the perpendicular distance from the corner of the triangle to the opposite side if all the sides 25cm long
calculate