Need homework help for my 12 year old....

Question

Here is the problem he is working on:

This table shows some terms of an arithmetic sequence. The sum of the first n terms is 2,464.

What is the nth term?

n 1. 2. 3. 4. 5. 6. 7.

an. - 19. - - 31. - 39

possible answers:

a) 601

b) 143

c) 139

d) 62

pretty sure the numbers one thru seven are 15,19,23,27,31,35,39

can you help out?

Answer 1

use Gauss' formula n(n+1)/2 = sum of 1 through n = 2464, solve for n

n^2 +n - 4928= 0

n=-1/2 + (1/2)sqr(1+ 4(4928))

=- .5 +.5sqr19713

= about 70.2-.5 = 69.7

an =nth term = a1+d(n-1) = 1+1(about 70) = about 71

"best" answer is 62, but none are correct and there's a problem with the problem, misprinted or miscopied