Give an EXPLICIT formula for the sequence 15,11,7,3....?

Answer 1

Each term goes down by 4, so there's a -4x in the formula.
f(x) = -4x + (some number)... call it n.

The first term f(1) = 15.
f(1) = -4(1) + n
15 = -4(1) + n
15 = -4 + n. Adding 4,
19 = n.

Your formula for f(x) = -4x + 19.

Answer 2

the 1st one provides 4 extra each and every time than the final, so: n-a million ? ( 4·(ok - a million) + 6 ) ok=a million which provides: n-a million ? ( 4·ok + 2 ) ok=a million in case you evaluate this sum, it supplies: = 4·(n - a million)(n - a million + a million)/2 + 2·(n - a million) = 2·(n - a million)(n) + 2·n - 2 = 2·n² - 2·n + 2·n - 2 = 2·n² - 2 this is your specific formulation: a = 2·n² - 2 - - - - the less demanding way works in case you comprehend calculus: the cost of exchange of the cost of exchange will enhance via 4 for each step: y'' = 4 combine: ?y''dx = y' = 4·x + C, combine back: ?y'dx = y = 2·x² + C,·x + C,, you comprehend positions, so resolve for C, and C,, 0 = 2·(a million)² + C,·(a million) + C,, 0 = 2 + C, + C,, C,, = -2 - C, 6 = 2·(2)² + C,·(2) + ( -2 - C, ) 6 = 8 + 2·C, - 2 - C, 6 = 6 + C, 0 = C, C,, = -2 - 0 = -2 this promises: y = 2·x² + (0)·x + (-2) y = 2·x² - 2 this is the comparable effect as above. —————————————————————————————————————— in case you check out the 2nd, you will discover that the transformations are: 7, 19, 37, sixty one, ... The transformations between those factors are: 12, 18, 24, ... And between those transformations, you have: 6, 6, ... So the cost of exchange of the cost of exchange of the cost of exchange... is continuous. this suggests the third spinoff is continuous: d³y/dx³ = y''' = 6 ??? 6 dx³ Integrating this 3 times supplies a cubic equation: y = x³ + a·x² + b·x + c (word that the 6 is canceled out via dividing via 2 for x² after which 3 for x³) utilising 3 factors to unravel for a, b, and c supplies: a + b + c = 2 4·a + 2·b + c = 2 9·a + 3·b + c = 2 fixing this technique of equations supplies: a = 0, b = 0, c = 2 even in spite of the incontrovertible fact that, considering the fact that all of us comprehend that it quite is moving at a relentless fee on the cubic point, then it quite is obvious that the constants for x² and x are 0. in any different case, it does no longer have a relentless fee of exchange at that time. — — — — — — — — — — — — — — — — for that reason the categorical formulation is: a = n³ + 2 —————————————————————————————————————— locate the adjustments for the third: -8, -a million, 18, fifty 5, 116, ... 7, 19, 37, sixty one, ... 12, 18, 24, ... 6, 6, 6, ... back, the third spinoff is 6 right here. so which you in simple terms decide for to alter the beginning element. y = ??? 6 dx³ y = x³ + C -8 = (a million)³ + C C = -8 - a million= -9 — — — — — — — — — — — — — — — — the categorical formulation is: a = n³ - 9

Answer 3

the number you are trying to find is y. X is the order in the sequence minus 1 (like 15 is first so its 0, 11 is 1 ect.)

so the answer should be
y=15-(x4)

Answer 4

The jth term is given by
Tj = 15 - 4*(j-1)

Answer 5

x-4

Answer 6

t= -4x+19
?