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3 years ago

Which is an equation for the nth terms of the sequence 12,15,18,21

2 answers:

7 0

$\bf 12~~,~~\stackrel{12+3}{15}~~,~~\stackrel{15+3}{18}~~,~~\stackrel{18+3}{21}~\hspace{10em}\stackrel{\textit{common difference}}{d=3} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=12\\ d=3 \end{cases} \\\\\\ a_n=12+(n-1)3\implies a_n=12+3n-3\implies a_n=3n+9$

GalinKa [24]3 years ago

7 0

Answer:

tₙ = 3(3 + n)

Step-by-step explanation:

Points to remember

nth term of an AP

tₙ = a + (n - 1)d

Where a - first term of AP

d - Common difference of AP

To find the nth term 

The given series is,

12,15,18,21 .....

Here a = 12 and d = 15 - 12 = 3

tₙ = a + (n - 1)d

= 12 + (n - 1)3

=12 + 3n - 3

= 9 + 3n

= 3(3 + n)

Therefore tₙ = 3(3 + n)

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The graph of a linear system is shown

nirvana33 [79]

Answer:

The coordinates of the point of intersection is (2, 7)

Step-by-step explanation:

From the graph, we have the two intersecting straight lines each described as follows;

The first straight line graph from the left, we have;

y-intercept = (0, 5), x-intercept = (-5, 0) therefore, the slope, m = (0 - 5)/(-5 - 0) = 1

The equation of the graph is slope-intercept form is y - 5 = 1×(x - 0)

Which gives;

y = x + 5.........................(1)

The second lie graph has y-intercept = (0, 9), x-intercept = (9, 0) therefore, the slope, m = (0 - 9)/(9 - 0) = -1

The equation of the graph in slope-intercept form is y - 9 = -1×(x - 0)

Which gives;

y = -x + 9.......................(2)

To find the point of intersection, we equate equation (1) to equation (2), which are the y-value function of x, we have;

x + 5 = -x + 9

x + x = 9 - 5

2·x = 4

x = 4/2 = 2

x = 2

From either equation (1) or equation (2), we can find the value of y as follows;

y = -x + 9, where x = 2 gives;

y = -2 + 9 = 9 - 2 = 7

y = 7

The coordinates of the point of intersection is (2, 7).

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3 years ago

What is the value of log2 128?

DedPeter [7]

If you get confused by logarithms, here's an easier way to think about this problem: What power of 2 equals 128? Well, we know 2^3 = 8, then 2^4 must equal 16. Doubling every times, we get 2^5 = 32, 2^6 = 64 and 2^7 = 128. So, the value of log₂128 is 7.

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3 years ago

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d1i1m1o1n [39]

Answer:

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Step-by-step explanation:

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3 years ago

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makkiz [27]

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4 years ago

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vladimir2022 [97]

Answer:

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Step-by-step explanation:

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