What is the nth term 4 11 20 31 44 59?

Answer 1

The interval grows by 2 for each term so this is a geometric sequence involving a n² somewhere.
x0=4
x1=x0+7 x1=4+(5+2(1))
x2=x1+9 x2=4+(5+2(1))+(5+2(2))
x3=4+(5+2(1))+(5+2(2))+(5+2(3))
rearranging
x3=4+(5+5+5)+(2(1)+2(2)+2(3))
The end of this is the triangular sequence, so...
xn=4+5n+2(n2+n)/2
collecting terms and simplifying...
xn=4+5n+(n2+n)
xn=n2+6n+4 ■

Answer 2

The given sequence is an arithmetic sequence where the common difference between consecutive terms is increasing by 1 each time. The nth term of an arithmetic sequence can be found using the formula: ( a_n = a_1 + (n-1)d ), where ( a_n ) is the nth term, ( a_1 ) is the first term, ( n ) is the position of the term in the sequence, and ( d ) is the common difference. In this case, the first term ( a_1 = 4 ) and the common difference ( d = 7 ) (as it increases by 1 each time). Therefore, the nth term can be calculated as ( a_n = 4 + (n-1)7 = 7n - 3 ).

Answer 3

Well, darling, the nth term of this sequence is n² + 3. So, if you plug in n = 1, 2, 3, 4, 5, you'll get 4, 11, 20, 31, 44, just like you asked. Just remember, math may be a pain in the rear, but it's always there to keep you on your toes.