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Romashka-Z-Leto [24]
3 years ago
14

An arithmetic sequence is defined by the general term tn = -5 + (n - 1)78, where n ∈N and n ≥ 1. What is the recursive formula o

f the sequence?
Pleeeeaaseee help
Mathematics
1 answer:
GrogVix [38]3 years ago
5 0

\text{The general term of an arithmetic sequence:}\ a_n=a_1+(n-1)d\\\\a_n-n-th\ term\\a_1-first\ term\\d-common\ difference\\\\\text{We have}\ t_n=-5+(n-1)78.\ \text{Therefore}\ t_1=-5\ \text{and}\ d=78\\\\\text{The recursive formula of the sequence:}\\\\\left\{\begin{array}{ccc}t_1=-5\\t_n=t_{n-1}+78\end{array}\right

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Answer:

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Step-by-step explanation:

Speed = \frac{distance}{time}

Sarah's speed = 6 km/hr = 1.6667 m/s

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The measure of angle between their bearings = 105^{o}

After 30 minutes (1800 seconds);

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Sarah would have covered a distance = 1.6667 x 1800

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Emily would have covered a distance = 2.7778 x 1800

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The distance between them, a, can be determined by applying the cosine rule;

a^{2} = b^{2} + c^{2} - 2bcCos A

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a = \sqrt{41764000}

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a = 6462.5 m

The distance between them after 30 minutes is 6.5 km.

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