What are the first four terms of a geometric sequence if the common ratio is 10 and the first term is 4.5? A.4.5, .45, .045, .0045
B.4.5, 9.0, 13.5, 18.0
C.4.5, 14.5, 24.5, 34.5
D.none of the above
I think this is D...?
Unit 5 lesson 1 sequences
1. C
2. B
3. C
4. B
5. D
Great...thanks
you are welcome x three
hal is right for the unit 5 functions lesson 1 sequences quick check
so keep multiplying by 10 ...
4.5 45 450 4500 45000 ....
I don't see the correct choice, so .....
first term, a = 4.5
common ratio, r = 10
the general form of a geometric sequence is
a , a r , a r ©÷ , a r ©ø , .......... , a r ©ú
.................>>>...where a is the first term,
.................>>>...r is the common ratio,
.................>>>...nth term = a r ^ ( n - 1 )
1st term, a = 4.5
2nd term = a r = ( 4.5 ) ( 10 ) = 45
3rd term = a r ©÷ = ( 4.5 ) ( 10 ) ©÷ = ( 4.5 ) ( 100) = 450
4th term = a r ©ø = ( 4.5 ) ( 10) ©ø = ( 4.5 ) ( 1,000 ) = 4500
5th term = a r^4 = ( 4.5 ) ( 10 )^4 = ( 4.5 ) ( 10,000 ) = 45000
Answer D - none of the above! :)
To find the first four terms of a geometric sequence, you can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
Where:
an = the nth term of the sequence
a1 = the first term of the sequence
r = the common ratio of the sequence
n = the position of the term in the sequence
In this case, the common ratio (r) is 10 and the first term (a1) is 4.5.
Let's calculate the first four terms using the given values:
For n = 1:
a1 = 4.5
a1 = 4.5 * 10^(1-1) = 4.5 * 10^0 = 4.5
For n = 2:
a2 = 4.5 * 10^(2-1) = 4.5 * 10^1 = 45
For n = 3:
a3 = 4.5 * 10^(3-1) = 4.5 * 10^2 = 450
For n = 4:
a4 = 4.5 * 10^(4-1) = 4.5 * 10^3 = 4500
So, the first four terms of the geometric sequence with a common ratio of 10 and a first term of 4.5 are: 4.5, 45, 450, 4500.
Now, let's compare these terms with the given options:
A. 4.5, 0.45, 0.045, 0.0045 - These terms are incorrect.
B. 4.5, 9.0, 13.5, 18.0 - These terms are incorrect.
C. 4.5, 14.5, 24.5, 34.5 - These terms are incorrect.
D. none of the above - This is the correct answer because none of the given options match the calculated terms of the geometric sequence.
Therefore, the correct answer is D.