Mathematics, 25.09.2020 09:01, jady20krazy

Find an example of an arithmetic sequence that has an explicit pattern. Then determine the formula for that sequence and use it to define the given term.

Find an example of an arithmetic sequence that has an explicit pattern. Then determine the formula

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answered: crtlq

11)

5, -5, -15, -25, ...

-5-5 = -10; -15-(-5) = -10; -25-(-15) = -10 ⇒ this is an example of arithmetic sequence that has explicit patern (evey next term is 10 less than previous one)

difference: d = -10

first term: a = 5

so the formula:

$a_n=a+d(n-1)\\\\a_n=5+(-10)(n-1)\\\\a_n =5-10n+10\\\\\underline{a_n=-10n+15}$

and:

$a_{20}=-10\cdot20+15=-200+15=-185$

12)

19, 26, 33, 40, ...

26-19 = 7; 33-26 = 7; 40-33 = 7 ⇒ this is an example of arithmetic sequence that has explicit patern (evey next term is 7 more than previous one)

difference: d = 7

first term: a = 19

so the formula:

$a_n=a+d(n-1)\\\\a_n=19+7(n-1)\\\\a_n =19+7n-7\\\\\underline{a_n=7n+12}$

and:

$a_{39}=7\cdot39+12=273+12=285$

13)

-20, -29, -38, -47, ...

-29-(-20) = -9; -38-(-28) = -9; -47-(-38) = -9 ⇒ this is an example of arithmetic sequence that has explicit patern (evey next term is 9 less than previous one)

difference: d = -9

first term: a = -20

so the formula:

$a_n=a+d(n-1)\\\\a_n=-20+(-9)(n-1)\\\\a_n =-20-9n+9\\\\\underline{a_n=-9n-11}$

and:

$a_{12}=-9\cdot12-11=-108-11=-119$

11)

1, -2, 3, -4, ...

-5-1 = -3; 3-(-2) = 5 ≠ -3 ⇒ this is NOT an example of arithmetic sequence

however it has explicit patern:

$a_1=1 =1\cdot\left(-1\right)^0= 1\cdot\left(-1\right)^{1-1}\\\\a_2=-2=2\cdot\left(-1\right)^1=2\cdot\left(-1\right)^{2-1}\\\\a_3=3=3\cdot\left(-1\right)^2=3\cdot\left(-1\right)^{3-1}\\\\a_4=-4=4\cdot\left(-1\right)^3=4\cdot\left(-1\right)^{4-1}\\\\\underline{a_n=n\cdot\left(-1\right)^{n-1}}$

so:

$a_{33}=33\cdot\left(-1\right)^{33-1}=33\cdot\left(-1\right)^{32}=33\cdot1=33$

answered: Guest

98 points djdjsi zisksis sjsjsi sisksj sksjdj sksks sjsisj

answered: Guest

Ok here we go ..there are plenty of ways to solve such math problems but we will go for the smartest and easiest ..5x+2y=7 -2x+6y=9we rearrange them into the following ..by multiplying the 1st equation by 2 it becomes 10x + 4y = 14we rearrange it and so it becomes 10x = 14 - 4yas for the second equation we multiply it by 5 and rearrange it so it becomes as to the following ..-10x + 30y = 45rearranging so 10x = 30y -45now 10x equals both 14 - 4y and 30y -45so 14 - 4y = 30y -4531 = 26yy= 31/26 = 1.19 or around 1.2so by now we can calculate x easily as -2x+6y=9so 2x = 6y -9 = 6 * 31/26 - 9 = -1.84 then x = - 0.92 or around -0.9best luck!

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