Question

What is the position on 999 in the sequence represented by the nth term n3-1

Answer 1

Answer:

nth term is n^3 - 1

it's given 999 is term of this sequence

so, n^3 - 1 = 999

n^3 = 1000

n = 10. ( cube root of 1000 is 10)

999 is 10th term of sequence

Answer 2

Step-by-step explanation:

$T_{1} = {n}^{3} - 1 \\ T_{1} = {1}^{3} - 1 \\ T_{1} = 1 - 1 \\ T_{1} = 0 \\ \\ T_{2} = {2}^{3} - 1 \\ T_{2} = 8 - 1 \\ T_{2} = 7 \\ \\ T_{3} = {3}^{3} - 1 \\ T_{3} = 27 - 1 \\ T_{3} = 26 \\ \\ The \: \: Sequence \: \: is : \\ 0, \: \: 7, \: \: 26, \: ... \: 999 \\ \\ T_{n} = {n}^{3} - 1 \\ 999 = {n}^{3} - 1 \\ 999 + 1 = {n}^{3} \\ 1000 = {n}^{3} \\ 1000 = {10}^{3} \\ \boxed{n = \underline{ \underline{ 10}}} \\ \\ ∴ \: \: {\bf{10}^{th} \: \: Term} \: \: of \: \: the \: \: Sequence \: \: is \: \: {\bf999}$