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Mathematical equation with a series of numbers: 4, 9, 14, 19, 24, ...
Recursive formula: aₙ = aₙ₋₁ + 5
Next term: 29

Write a recursive formula for the sequence 4, 9, 14, 19, 24, ... Then find the next term.

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Illustration of a calculator displaying the sum 295,290

Find the sum of the sequence 5+15+45 + ...+ 295245

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Digital illustration showing an arithmetic series with the given characteristics: starting from 16, each term decreases by 9, and the series consists of 18 terms.

Find the sum of the arithmetic series with the following characteristics: a1= 16, d = –9, n = 18

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Digital image displaying an arithmetic series, with the numbers written out and highlighted: 27, 54, 81, 108, ..., 540, with a corresponding equation to find the sum of the series.

Find the sum of the arithmetic series: 27 + 54 + 81 + 108 + ... + 540

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Mathematical notation expressing the geometric series: "a₁ = 86185 / (2^10)"

Find a1 for the given geometric series: Sn = 86185, r = 2, n = 10

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Digital illustration showing a sequence of numbers magnifying: 4, 12, 36

Find the general term of the following 4, 12, 36,

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Visualization of a decreasing sequence with 42, 38, 34, ... displayed as arrow symbols pointing downwards

Find the general term of the following 42, 38, 34, ...

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Close-up image of a math equation with variables "a" and "d" representing the first term and common difference in the arithmetic sequence

In an arithmetic sequence, t5 = 8 and t31 = - 44. Find "a" and "d"

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Graphical representation of a geometric sequence with the 7th term being -192 and the 15th term being -49152

In a geometric sequence, t7 = -192 and t15 = - 49152. Find "a" and "r".

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Graph showing the displacement of the buoy over time, indicating the second time it returns to the center

The displacement of a buoy, in metres, in the water is described by the function b(t) = 5sin(30t) at time t seconds. If the buoy starts at the center, when is the second time that the buoy will be back at the center?

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Visualization of Ryan Gosling jumping on a trampoline, with a label showing "1.5m" representing the height from the ground

Ryan Gosling is jumping on a trampoline. His distance from the ground, in metres, in terms of time, is modelled by the equation h(s) = 0.75cos(180s)° + 1.5. What does the 1.5 in this equation represent?

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Diagram of a spring hanging vertically with an arrow pointing from the lowest point (rest position) to the furthest point reached (maximum displacement)

A spring bounces up and down according to the model d(t) = 4cos(30t) − 1, where d(t) is the displacement in cm from the rest position and t is time in seconds. What is the range?

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