If a_n = 4(3)^n−1 , what is S_3?
Select one:
a. 12
b. 36
c. 16
d. 52
the answer is D u are welcome
D. a_n = 9 − 6(n − 1) where n ≥ 1
The answer is D, but I don't recognize that formula.
It is clearly a linear function, or an arithmetic sequence.
a_n = 4 * 3n-1
That is a geometric sequence with
a = 4
r = 3
S_3 = 4(3^3-1)/(3-1) = 4(26/2) = 52
To find the value of S_3, we first need to determine the general term of the sequence a_n. From the given information, we have a_n = 4(3)^n−1.
To find S_3, we need to add up the first three terms of the sequence a_n. In other words, we are calculating a_1 + a_2 + a_3.
Now let's substitute the values of n into the general term to find each term of the sequence:
a_1 = 4(3)^1−1 = 4(3)^0 = 4(1) = 4
a_2 = 4(3)^2−1 = 4(3)^1 = 4(3) = 12
a_3 = 4(3)^3−1 = 4(3)^2 = 4(9) = 36
Now, let's add up the terms:
a_1 + a_2 + a_3 = 4 + 12 + 36 = 52
Therefore, the value of S_3 is 52.
The correct answer is d. 52.