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schepotkina [342]
3 years ago
11

A supermarket finds that the number of boxes of a new cereal sold increases each week. In the first week, only 16 boxes of the c

ereal were sold. In the next week, 33 boxes of the cereal were sold and in the third week 50 boxes of the cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.
What is the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n?


an=17n−1

​​an=17n+33

​an=17n+1

an=17n−33
Mathematics
1 answer:
notsponge [240]3 years ago
6 0

Answer:

an = 17n-1

Step-by-step explanation:

have a good day T_T

:O :P

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What is the smallest integer $n$, greater than $1$, such that $n^{-1}\pmod{130}$ and $n^{-1}\pmod{231}$ are both defined?
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First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.

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130 = 2 • 5 • 13

231 = 3 • 7 • 11

so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.

To verify the claim, we try to solve the system of congruences

\begin{cases} 17x \equiv 1 \pmod{130} \\ 17y \equiv 1 \pmod{231} \end{cases}

Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:

130 = 7 • 17 + 11

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231 = 13 • 17 + 10

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so that y = 68.

3 0
3 years ago
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