Find S(sub 73) for the arithmetic series 4 + 7 +10....
you have a AS where
a = 4, d = 3 and n = 73
sum(73) = (73/2)(2(4) + 72(3))
= (73/2)( 224) = 8176
To find the sum S₇₃ of an arithmetic series, we first need to determine the first term (a₁), the common difference (d), and the number of terms (n).
In this case, the first term a₁ is 4, and the common difference d is (7 - 4 =) 3. The nth term can be found using the formula:
aₙ = a₁ + (n - 1) * d
To find the number of terms (n), we can use the formula:
aₙ = a₁ + (n - 1) * d
10 = 4 + (n - 1) * 3
10 - 4 = 3n - 3
6 = 3n - 3
3n = 9
n = 3
Therefore, the number of terms (n) is 3.
Now we can calculate the sum S₇₃ using the formula:
Sₙ = (n / 2) * (2a₁ + (n - 1) * d)
S₇₃ = (3 / 2) * (2 * 4 + (3 - 1) * 3)
S₇₃ = (3 / 2) * (8 + 2 * 3)
S₇₃ = (3 / 2) * (8 + 6)
S₇₃ = (3 / 2) * 14
S₇₃ = (3 / 2) * 14
S₇₃ = 21
Therefore, the sum of the arithmetic series 4 + 7 + 10 + ... up to the 73rd term is 21.