The nth term of a sequence is 3n2 what is the term in the sequence with a value greater with 1000

19 > 1083

Step-by-step explanation:

Given: The nth term of a sequence is given by .  

let βn be the nth term.

           then βn = 3n²

Let x be the term which is the first one with a value greater than 1000.

19 th term is the first one with a value greater than 1000 the sequence that is βx > 1000

         3x² > 1000

divide by 3

           3x²/3 > 1000/3

            x² > 1000/3

            x² > 333.33

to make x the subject of the formula, square root both sides

√x² > √333.333

the square cancel the square root at x

x > √333.333

x>18.257

x > 19 approximately

19 th term is the first one with a value greater than 1000 the sequence.

that is: β19 = 3(19)²

            3(316)²

               =1083.

Hope it will help.

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).