Question 20 If a, b and c are in A.P., and a + b + c = nb, what is the value of n?
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If a, b and c are in A.P., and a + b + c = nb, what is the value of n?
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Answer: C. C) 3
Since a, b, c are in A.P., a + c = 2b. Thus a + b + c = 2b + b = 3b, which means n = 3.
Step-by-step Derivation:
Step 1: For three terms in arithmetic progression, the middle term is the arithmetic mean: b = (a + c)/2 => a + c = 2b.
Step 2: Substitute into sum: a + b + c = (a + c) + b = 2b + b = 3b.
Step 3: Comparing with nb gives nb = 3b => n = 3.