Write a rule for the nth term of the geometric sequence. Then find a7.
1. 7, -4.2, 2.52, -1.512, ...
7, -4.2, 2.52, -1.512, ...
Divide successive terms,
-4.2/7=-0.6
2.52/-4.2=-0.6
-1.512/2.52=-0.6
So the common ratio is r=-3/5
T(1)=7
T(n)=7r^n
T(7)=7(-3/5)^7
=-15309/78125
=-0.196 approx.
how do you
To find the rule for the nth term of a geometric sequence, we need to determine the common ratio (r).
By observing the given sequence, we can see that each term is obtained by multiplying the previous term by the same number.
To find this common ratio (r), we can divide any term of the sequence by its preceding term:
-4.2 ÷ 7 = -0.6
2.52 ÷ (-4.2) = -0.6
-1.512 ÷ 2.52 = -0.6
As we can see, the common ratio is -0.6.
Therefore, the rule for the nth term of this geometric sequence is given by:
an = a1 * r^(n-1)
In this case, a1 = 7 and r = -0.6. Thus, the rule is:
an = 7 * (-0.6)^(n-1)
To find a7, we substitute n = 7 into the formula:
a7 = 7 * (-0.6)^(7-1)
a7 = 7 * (-0.6)^6
a7 ≈ 1.131
To find the nth term of a geometric sequence, we need to determine the common ratio.
In this sequence, we start with 7 and multiply each term by -0.6 to get the next term. Therefore, the common ratio is -0.6.
The formula for the nth term of a geometric sequence is:
an = a1 * r^(n-1)
Where:
an = the nth term of the sequence
a1 = the first term of the sequence
r = the common ratio
n = the position of the term in the sequence
In this case, a1 = 7, r = -0.6, and we want to find a7. Plugging these values into the formula, we have:
a7 = 7 * (-0.6)^(7-1)
a7 = 7 * (-0.6)^6
Evaluating this expression gives us the value of a7.