This number 325^3 has a long sequence of positive consecutive integers that sum up to 325^3. The average of the first term plus the 999th term and the 5000th term is 2,162. What are the first term, last term and the number of terms of this sequence? Thank you for help.

Guest Aug 2, 2019

#1**0 **

Since 2,162 is the average of the 3 terms, therefore we have: 3 x 2,162 =6,486

6,486 - (5000 - 1) - (999 - 1) =489 - this is 3 times the first term.

489 / 3 = 163 - this is the first term.

N/2 * [2 * 163 + (N - 1)] =325^3, solve for N

N =8,125 - this is the number of terms.

Last term =8,125 + 163 - 1 = 8,287 - this is the last term.

Sum=[163 + 8,287] / 2 * 8,125 = 325^3

Guest Aug 2, 2019