Question

The 3rd and 7th terms of an A.P are -1 and 11 respectively. Fine the nth term and the numbers of which must be added to get a sum of 430

Answer 1

a+2d = -1
a+6d = 11
subtract them:
4d = 12
d = 3
from a+2d = -1 , a = -7

term(n) = a+(n-1)d
= -7 + 3(n-1)
= -7 + 3n - 3
= 3n - 10

"the numbers of which must be added to get a sum of 430"

I will assume you mean, "how many terms are needed to have sum of 430" ?

sum(n) = (n/2)(first + last)
430 = (n/2)(-7 + 3n-10)
860 = n(3n - 17)
3n^2 - 17n - 860 = 0
(n - 20)(3n + 43) = 0

n = 20 or n = -43/3, the latter would be extraneous

you will need 20 terms

Answer 2

Haule