Find the 50th term sequence 5 , -2 , -9 , -16

2 answers:

7 0

5 - 7 = - 2 ;
- 2 - 7 = - 9 ;
-9 - 7 = -16 ;
"common difference" d is - 7 ;
The n-th term of an arithmetic sequence is of the form an = a1 + (n – 1)d ;
a50 = 5 + 49 × ( - 7 ) = 5 - 343 = - 338;

Wittaler [7]2 years ago

7 0

The 50th therm of the sequence is -338

So therefor the answer is -338

You might be interested in

PLS HELP WILL MARK BRAINIEST!!!!TY

Leni [432]

Answer:

hope this heps and pls mark brainliest :))

Step-by-step explanation:

5 0

2 years ago

The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$