what are the first four terms of a geometric sequence if the common ratio is 10 and the first term is 4.5
4.5 .45 .045 .0045
4.5 9.0 13.5 18.0
4.5 14.5 24.5 34.5
none of the above
To determine the first four terms of a geometric sequence with a common ratio of 10 and a first term of 4.5, you can use the formula:
an = a * r^(n-1)
Where:
an is the nth term of the sequence
a is the first term
r is the common ratio
n is the position of the term
Let's calculate the first four terms:
a1 = 4.5 * 10^(1-1) = 4.5 * 10^0 = 4.5 * 1 = 4.5
a2 = 4.5 * 10^(2-1) = 4.5 * 10^1 = 4.5 * 10 = 45
a3 = 4.5 * 10^(3-1) = 4.5 * 10^2 = 4.5 * 100 = 450
a4 = 4.5 * 10^(4-1) = 4.5 * 10^3 = 4.5 * 1000 = 4500
Therefore, the first four terms of the geometric sequence are 4.5, 45, 450, and 4500. Hence, none of the options provided (4.5, 0.45, 0.045, 0.0045) is correct.