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muminat
3 years ago
7

What are the first three terms of the sequence represented by the recursive formula

Mathematics
1 answer:
AnnyKZ [126]3 years ago
5 0
Explecit formula
hmm, seems to be a geometric sequence
so
an=a1+d(n-1)
d=common differnce
a1=first term

given
a1=firstterm=9.2

and the difference between each tierm is 1.8

an=9.1-1.8(n-1) is da equation

so 4th option
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The sum of squares of two consecutive odd numbers is 514 find the numbers ​
amid [387]

Correct Question : The sum of squares of two consecutive positive odd numbers is 514. Find the numbers.

\rule{130}1

Solution :

Let the two consecutive positive odd numbers be x and (x + 2)

\rule{130}1

☯ \underline{\boldsymbol{According\: to \:the\: Question\:now :}}

:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup

When,

\bullet\: \textsf {x = } \textbf {15}

\bullet\: \sf x + 2 = 15 + 2 =\textbf{ 17}

\therefore\:\underline{\textsf{The required positive integer is \textbf{15 and 17}}}.

5 0
3 years ago
a water tank is draining at a constant rate if after five minutes the tank is drained by 4.5 gallons what is the rate in gallons
vova2212 [387]

Answer:

The rate is 0.9 gallon per minute

Step-by-step explanation:

Here, we have 4.5 gallons drained in 5 minutes but we are interested in calculating the rate per minute

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8 0
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