    Question

# Sort the arithmetic means (AM) of the given APs in ascending order if each AP consist of 11 terms.

A
1, 3, 5,...
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B
-10, -5, 0,...
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C
-2, 0, 2,...
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D
12, 12, 12,...
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Solution

## The correct option is The arithmetic mean of an AP is given by ⟹AM=Sum of all termsNumber of terms in the AP. If a and d are the first term and the common difference of the AP respectively, then we have AM=Sn2=n2×(2a+(n−1)d)n=2a+(n−1)d2, where Sn denotes the sum to n terms of the AP. Given that n=11 for all the APs. In the AP 1, 3, 5,... a=1 and d=a2−a1=3−1=2. ∴AM=2a+(n−1)d2 =2(1)+(11−1)22 =11 In the AP -10, -5, 0,...we have a=−10 and d=5. ∴AM=2a+(n−1)d2 =2(−10)+(11−1)52 =15 Using the exact same procedure, we get AM = 8 for the AP -2, 0, 2,... and AM=12 for the AP 12, 12, 12,... Hence, AM of -2, 0, 2,... < AM of 1, 3, 5,... < AM of 12, 12, 12,... < AM of -10, -5, 0,...  Suggest Corrections  0      Similar questions  Related Videos   MATHEMATICS
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