Question

1.) in the fibonacci sequence each term after the first two terms is the sum of the preceding two terms. If the first two terms are 1 and 1, then what is the tenth term?

2.) Find the geometric mean of 275 and 11

Answer 1

1. the tenth term is 55
2. geometric mean is 55

Answer 2

1) Tenth term of the Fibonacci sequence is 55.

2) The geometric mean of 275 and 11 is 55.

Explanation:

1) Fibonacci sequence is a sequence in which each term after the first two terms is the sum of the preceding two terms.

Given: the first two terms are
`a_1=1` and
`a_2=1`

We have to find the tenth term of the Fibonacci sequence.

Adding first two terms,

`a_1+a_2=1+1=2=a_3`

`a_2+a_3=1+2=3=a_4`

`a_3+a_4=2+3=5=a_5`

`a_4+a_5=5+3=8=a_6`

`a_5+a_6=5+8=13=a_7`

`a_6+a_7=8+13=21=a_8`

`a_7+a_8=13+21=34=a_9`

`a_8+a_9=34+21=55=a_(10)`

Thus, tenth term of the Fibonacci sequence is 55.

b) To find the geometric mean of 275 and 11.

Geometric mean is a mean where we take the product of numbers and then take the nth root (n is the number of terms )

Geometric mean of two numbers a and b is
`√(ab)`

Here, a = 275 and b = 11

`a * b=275*11=3025`

Thus, the geometric mean of 275 and 11 =
`√(275*11)=√(3025)=55`

Thus, the geometric mean of 275 and 11 is 55.