whats the nth term for

Question

2, 10, 24, 44, 70

Answer 1

The sequence is 2, 10, 24, 44, 70, ..............

The formula 3n^2 - n generates the a sequence of numbers as follows :

n = 1            3n^2 - n = 3( 1 )^2 - 1 = 3 - 1 = 2

n = 2            3n^2 - n = 3( 2)^2 - 2 = 12 - 2 = 10

n = 3            3n^2 - n = 3( 3 )^2 - 3 = 27 - 3 = 24

n = 4            3n^2 - n = 3( 4 )^2 - 4 = 48 - 4 = 44

n = 5            3n^2 - n = 3( 5 )^2 - 5 = 75 - 5 = 70

etc.

So, the formula generates the sequence 2, 10, 24, 44, 70, .............. etc.

Therefore, the n th term of the given sequence is 3n^2 - n.

Answer 2

Sequence : An ordered list of numbers (or) A sequence is a list of numbers in a particular order.

Series : The sum of an ordered list of numbers (or) A series is an indicated sum of the terms of a sequence.

Arithmetic Sequence : A sequence of numbers with a common difference between any two consecutive terms.

Arithmetic Series : The sum of terms in an arithmetic sequence.

Geometric Sequence : A sequence of numbers with a common ratio or multiplier between any two consecutive terms.

Arithmetic Series : The sum of terms in an geometric sequence.

The numbers are 2, 10, 24, 44, 70, .......... n.

The above numbers are do not follow the particular order, so this is not a sequence.

This is may be series.

To check the series is arithmetic or geometric as follows.

Here the common difference d₂ = 6.

Arithmetic sequence :

Arithmetic series :

The sum S_n of the first n terms of an arithmetic series is given by , where t₁ = first term = 2, t_n = last term = n and d = common difference = 6.

.

Check :

n = 1           s₁ = 3n^2 - n = 3( 1 )^2 - 1 = 3 - 1 = 2.

n = 2           s₂ = 3n^2 - n = 3( 2)^2 - 2 = 12 - 2 = 10.

n = 3           s₃ = 3n^2 - n = 3( 3 )^2 - 3 = 27 - 3 = 24.

n = 4           s₄ = 3n^2 - n = 3( 4 )^2 - 4 = 48 - 4 = 44.

n = 5           s₅ = 3n^2 - n = 3( 5 )^2 - 5 = 75 - 5 = 70. etc.