choose the correct option for the first and last numbers of 6^3 , as a sum of consecutive odd integers from the following.
Answer:
The first and last numbers of 6^3 are 1 and 216, respectively.
A sum of consecutive odd integers can be represented as follows:
(2n - 1) + (2n + 1) + (2n + 3) + … + (2n + 2m - 1) = m(2n + m - 1)
where m is the number of odd integers in the sum and n is the first odd integer in the sum.
To find m, we can use the equation m(2n + m - 1) = 216 and solve for m:
m(2n + m - 1) = 216
m(2n + m - 1) = 2^3 * 3^3
m(2n + m - 1) = 2^3 * (3^2) * 3
m(2n + m - 1) = 8 * 9 * 3
m(2n + m - 1) = 216
m(2n + m - 1) = 2^3 * 3^3
m = 6.
Since m is an integer, the number of odd integers in the sum is 6. The first odd integer in the sum would be (2n - 1), where n = (m + 1) / 2.
n = (6 + 1) / 2 = 3.5, which is not an integer, so there is no set of 6 consecutive odd integers that sums to 216.