Find the 51st term of the arithmetic sequence 29, 9, -11,...

Mathematics

1 answer:

mina [271]3 years ago

5 0

Answer:

Step-by-step explanation:

arithmetic sequences can be written as

$a_n = a_1 + (n-1)d$

$29 = a_1 + (1-1)d\\29 = a_1\\9 = 29 + (2-1)d\\9 = 29 + d\\d = -20\\a_n = 29 -20 (n-1)\\a_n = 29 - 20n+20\\a_n = -20n + 49\\\\a_51 = -20(51) + 49 = -951$

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valentinak56 [21]

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3 years ago

( 7x + 2x - 3x2 + 9x) + (5x + 8x2 - 6x2 + 2x - 5)

Elena-2011 [213]

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If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3

horrorfan [7]

Answer: The correct option is (B) 24 : 25.

Step-by-step explanation: Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.

We are to find the ratio of the area of R to the area of S.

Let 2x, 3x be the sides of rectangle R and y be the side of square S.

Then, according to the given information, we have

$\textup{Perimeter of rectangle R}=\textup{Perimeter of square S}\\\\\Rightarrow2(2x+3x)=2(y+y)\\\\\Rightarrow 5x=2y\\\\\Rightarrow \dfrac{x}{y}=\dfrac{2}{5}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Therefore, the ratio of the area of R to the area of S is

$\dfrac{2x\times3x}{y\times y}\\\\\\=\dfrac{5x^2}{y^2}\\\\\\=6\left(\dfrac{x}{y}\right)^2\\\\\\=6\times\left(\dfrac{2}{5}\right)^2~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\=\dfrac{24}{25}\\\\=24:25.$