what is the sum of the arithmetic sequence 3,9,15...if there are 24 terms? 1) 2,028 2) 1,452 3) 1,1728 4) 2,268
Mathematics · High School · Tue Nov 03 2020
Answered on
Given the arithmetic sequence:
3, 9, 15… up until n = 24
Find the total sum of the Arithmetic Sequence.
Solution:
We must first determine the 24th term of the arithmetic sequence then we can proceed with finding the sum. In order to find the 24th term, we will use the formula,
An = A1 + (n -1)d
Since we don't know the value of d or the common difference, we first subtract the 1st term to the 2nd term.
d = A2 - A1
d = 9 - 3
d = 6
We can now proceed in substituting the values to the given equation.
A24 = 3 + (24 -1)6
A24 = 3 + 138
A24 = 141
Since we now have the value of n = 24, we can now solve the total sum by using the formula
Total Sum = (a1 + an) n / 2
Total Sum = (3 + 141)24/2
Total Sum = 3456 / 2
Total Sum = 1728