what is 1, 9, 19, 31, 45, 61, in a sequence

Question

i need help on ixl thats why im asking.

Answer 1

1, 9, 19, 31, 45, 61

  +8+10+12+14+16 ....

Need a +2  increase on top of the common difference

 

A = n + (n-1)(d+n) 

 

Where n = 1,2,3,4,5,...

d = 5

 

1 = 1 + (1-1)(d+1)

 

9 = 2 + (2-1)(5+2)

 

19 = 3 + (3-1)(5+3)

 

31 = 4 + (4-1)(5+4)

 

45 = 5 + (5-1)(5+5)

 

 

Answer 2

Original sequence {a_n} for n=1,2,3,...:

 

1,9,19,31,45,61,...

 

First differences: Δa_n = a_n+1 - a_n.

 

8,10,12,14,16,...

 

Second differences: Δ²a_n = Δa_n+1 - Δa_n.

 

2,2,2,2,...

 

So the formula has the form a_n = An² + Bn + C.

 

A = 2/2! = 1.

 

a_n - n²: 0,5,10,15,20,25,...

 

B = 5,

 

a_n - n² - 5n: -5,-5,-5,-5,-5,-5...

 

C = -5

 

a_n = n² + 5n - 5