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Lynna [10]
3 years ago
15

If 63

%5C%3A%20then%20%5C%3A%20k%20%3D%20" id="TexFormula1" title=" {63}^{2} = 1 + 3 + 5 + ... + k \: then \: k = " alt=" {63}^{2} = 1 + 3 + 5 + ... + k \: then \: k = " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Scilla [17]3 years ago
3 0

Answer:

125

Step-by-step explanation:

let's see if we can find a pattern

1 = 1 = 1^2

1 + 3 = 4 = 2^2

1 + 3 + 5 = 9 = 3^2

we are starting to see a pattern here, when we add another term, we find the next integer squared.

we can find this last number in our sequence with 2x-1.

so in the next line we should find 4^2. if we plug 4 into 2x-1 we would expect the last term in the sum to be 7.

1 + 3 + 5 + 7 = 16 = 4^2

so 2*63 -1 = 126 - 1 = 125

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The question is in the picture.
dangina [55]
<h2><u>Part A:</u></h2>

Let's denote no of seats in first row with r1 , second row with r2.....and so on.

r1=5

Since next row will have 10 additional row each time when we move to next row,

So,

r2=5+10=15

r3=15+10=25

<u>Using the terms r1,r2 and r3 , we can find explicit formula</u>

r1=5=5+0=5+0×10=5+(1-1)×10

r2=15=5+10=5+(2-1)×10

r3=25=5+20=5+(3-1)×10

<u>So for nth row,</u>

rn=5+(n-1)×10

Since 5=r1 and 10=common difference (d)

rn=r1+(n-1)d

Since 'a' is a convention term for 1st term,

<h3><u>⇒</u><u>rn=a+(n-1)d</u></h3>

which is an explicit formula to find no of seats in any given row.

<h2><u>Part B:</u></h2>

Using above explicit formula, we can calculate no of seats in 7th row,

r7=5+(7-1)×10

r7=5+(7-1)×10 =5+6×10

r7=5+(7-1)×10 =5+6×10 =65

which is the no of seats in 7th row.

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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