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PIT_PIT [208]
3 years ago
8

Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d-6

Mathematics
1 answer:
kari74 [83]3 years ago
4 0

Answer: -209

Step-by-step explanation:

Formula for arithmetic progression

= a + (n - 1)d

Since a10 = 1 and d = -6

a10 = a + 9d

a + 9(-6) = 1

a - 54 = 1

a = 1 + 54

a = 55

Therefore, 45th term = a + (n - 1)d

= a + (45 - 1)d

= a + 44d

= 55 + 44(-6)

= 55 - 264

= -209

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4 years ago
When she checked the answer by estimating, it did not make sense. What error did Janice make?
Leokris [45]
<h2>Answer</h2>

Janice convert a mixed number to the wrong improper fraction

<h2>Explanation</h2>

To convert a mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and add the result to the numerator of the fraction; while keeping the denominator of the fraction as the denominator of the improper fraction.

Let's convert our mixed numbers to improper fractions:

To convert 10\frac{5}{6} we multiply the whole number 10 by the denominator of the fraction 6, and then we add the result to the numerator 5:

10\frac{5}{6} =\frac{(10*6)+5}{6} =\frac{60+5}{6} =\frac{65}{6}

Now let's convert 1\frac{2}{3}:

1\frac{2}{3}=\frac{(1*3)+2}{3} =\frac{3+2}{3} =\frac{5}{3}

Notice that Janice converted 1\frac{2}{3} as \frac{5}{2}, which is incorrect.

Since 1\frac{2}{3} =\frac{5}{3}, we can conclude that Janice convert a mixed number to the wrong improper fraction.

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