consider the sequence below

Question

the points 11,14,19,26,35

Answer 1

points indicate a quadradic function, y=x²+10

why? a test for quadradic behavior of values as x increases is

"differences of difference" is constant.

14-11=3,,,19-14=5,,,5-3=2

26-19=7,,,35-26=9,,,9-7=2

2 is the constant.

conclude y=ax²+bx+c

x=1 y=11,,11=a+b+c

x=2 y=14,,,14=4a+2b+c

x=3 y=19,,,19=9a+3b+c

eliminating c

have

3=3a+b

8=8a+2b

find a=1 and b=0

then c=10

Answer 2

You don't really specify what you want us to do with the sequence, but I do notice that you can use the following formula to represent the sequence: a_n = 10 + n²