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Anvisha [2.4K]
3 years ago
12

N/2 + 3 Find the first 5 terms in the sequence...

Mathematics
1 answer:
noname [10]3 years ago
4 0

Answer:

The first '5' terms of the given sequence

\frac{7}{2} , 4 ,\frac{9}{2} ,5,\frac{11}{2}

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given that the n^{th}    aₙ =     \frac{N}{2} + 3

<em>first term</em>

Put n=1  ⇒     \frac{1}{2} + 3 = \frac{7}{2}

<em>second term</em>

Put n=2 ⇒   \frac{2}{2} + 3 = 1+3=4

<em>Third term</em>

Put n=3 ⇒   \frac{3}{2} + 3 = \frac{3+6}{2}=\frac{9}{2}

<em>Fourth term</em>

Put n=4 ⇒  \frac{4}{2} + 3 = 2+3 =5

<em>Fifth term</em>

Put n=5 ⇒ \frac{5}{2} + 3 = \frac{5+6}{2}=\frac{11}{2}

The first '5' terms of the given sequence

\frac{7}{2} , 4 ,\frac{9}{2} ,5,\frac{11}{2}

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How can I find the complex roots of 125x^3+343. Please explain your steps
8_murik_8 [283]
First we assume that this is equal to zero

so what we notice is this is a sum of 2 perfect cube

recall that
a^3+b^3=(a+b)(a^2-ab+b^2)

125x^3+343=
(5x)³+(7)³=(5x+7)(25x²-35x+49)

now solve the part in second parenthasees because we can see that the first parenthasees (5x+7) is going to have a real root

remember quadratic formula

for ax^2+bx+c=0
x=\frac{-b+/- \sqrt{b^2-4ac} }{2a}
a=25
b=-35
c=49

x=\frac{-(-35)+/- \sqrt{(-35)^2-4(25)(49)} }{2(25)}
x=\frac{35+/- \sqrt{1225-4900} }{50}
x=\frac{35+/- \sqrt{-3675} }{50}
x=\frac{35+/- (\sqrt{3675})( \sqrt{-1}) }{50}
x=\frac{35+/- (\sqrt{3675})(i) }{50}
x=\frac{35+/- 35i\sqrt{3} }{50}
x=\frac{7+/- 7i\sqrt{3} }{10}

the comlex roots are

x=\frac{7+ 7i\sqrt{3} }{10} and \frac{7- 7i\sqrt{3} }{10}




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