In an arithmetic sequence {an}, if a1 = 5 and d = 3, the first 4 terms in the sequence are

2 answers:

6 0

A1 represents the first term

d represents the common difference.....and since the common difference is 3, u have to add 3 to each term to find the next term....because with an arithmetic sequence u add to find the next term, whereas, in a geometric sequence u multiply to find the next term

5...first term
5 + 3 = 8...2nd term
8 + 3 = 11...3rd term
11 + 3 = 14...4th term

ur answer is B

motikmotik3 years ago

5 0

$a_n=a_1+(n-1)d\\\\a_1=5;\ d=3\\\\substitute\\\\a_n=5+(n-1)\cdot3=5+3n-3=3n+2\\\\a_1=3\cdot1+2=5\\a_2=3\cdot2+2=8\\a_3=3\cdot3+2=11\\a_4=3\cdot4+2=14\\a_5=3\cdot5+2=17\\\vdot$

$Answer:\boxed{B)\ \{5;\ 8;\ 11;\ 14;\ 17;\ ... \} }$

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6 0

2 years ago

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avanturin [10]

In spherical coordinates, we have

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}$

which gives volume element

$\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

and so the triple integral is given by

$\displaystyle\iiint_H(9-x^2-y^2)\,\mathrm dV$
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$=\displaystyle2\pi\int_{\varphi=0}^{\varphi=\pi/2}\int_{\rho=0}^{\rho=2}(9\rho^2\sin\varphi-\rho^4\sin^3\varphi)\,\mathrm d\rho\,\mathrm d\varphi$
$=\dfrac{592\pi}{15}$