write an explicit formula for the sequence then find the fifth term
a_1 = 3, r = -3
a. a_n = 3*(-3)^n-1; 243
b. a_n = -3*(3)^n-1; -243
c. a_n = 3*(3)^n; 243
d. a_n = 3*(-3)^n; -729
thank u!!
To find the explicit formula for the given sequence with a first term of 3 (a_1) and a common ratio of -3 (r), we use the formula:
a_n = a_1 * r^(n-1)
Plugging in the values, we have:
a_n = 3 * (-3)^(n-1)
To find the fifth term (a_5), we substitute n = 5 into the formula:
a_5 = 3 * (-3)^(5-1)
= 3 * (-3)^4
= 3 * 81
= 243
Therefore, the explicit formula is a_n = 3 * (-3)^(n-1), and the fifth term is 243.
The correct answer is (a) a_n = 3*(-3)^(n-1); 243.
To find the explicit formula for the sequence, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 * r^(n-1),
where a_n represents the nth term, a_1 is the first term, r is the common ratio, and n is the term number.
In this case, we are given a_1 = 3 and r = -3. Plugging these values into the formula, we have:
a_n = 3 * (-3)^(n-1).
To find the fifth term (a_5), we substitute n = 5 into the formula:
a_5 = 3 * (-3)^(5-1).
Simplifying the exponent:
a_5 = 3 * (-3)^4.
Evaluating the term:
a_5 = 3 * 81.
Simplifying further:
a_5 = 243.
Therefore, the correct answer is option a:
a_n = 3 * (-3)^(n-1); fifth term (a_5) = 243.
for any geometric sequence a_n = a*r^(n-1)
so plug in your numbers.