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Anika [276]
4 years ago
7

The mean of 3 consecutive terms in an arithmetic sequence is 10, and the mean of their squares is 394. What is the largest of th

e 3 terms?
Mathematics
1 answer:
poizon [28]4 years ago
5 0
Let the numbers be:
a, a+b, a+2b
mean of the numbers is:
(a+a+b+a+2b)/3=10
(3a+3b)/3=10
a+b=10
thus second term is 10

The sum of square will be:
((10 - b)² + 10² + (10 + b)²<span>) / 3 = 394 
</span>(100 - 20b + b² + 100 + 100 + 20b + b²<span>) / 3 = 394
</span><span>(300 + 2b</span>²<span>) / 3 = 394
</span>(150+b²)=591
b²=441
b=-21,21

thus the numbers will be:
10-21, 10, 10+21
=-11,10,31
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