Consider the set of numbers a, 2a, 3a, ..., na where a and n are positive integers.

(a) Show that the expression for the mean of this set is.

(b) Let a = 4. Find the minimum value of n for which the sum of these numbers

exceeds its mean by more than 100.

Question

Mathematics

Meredith Villegas

5 April, 01:19

Consider the set of numbers a, 2a, 3a, ..., na where a and n are positive integers.

(a) Show that the expression for the mean of this set is.

(b) Let a = 4. Find the minimum value of n for which the sum of these numbers

exceeds its mean by more than 100.

+5

Answers (1)

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Sparkle · Answer 1

(a) The mean for this set is the total of the values divided by the number of values present in the set. That is,

average / mean = (a + 2a + 3a + ... + na) / n

(b) If a is 4, 2a = 8, na = 4n. Four the calculation,

(4 + 8 + ... + 4n) - ((4 + 8 + ... + na) / n) = 100

The value of n from the equation is approximately 7.8. The minimum value of n should be 8.

Consider the set of numbers a, 2a, 3a, ..., na where a and n are positive integers.(a) Show that the expression for the mean of this set is.(b) Let a = 4. Find the minimum value of n for which the sum of these numbersexceeds its mean by more than 100.

Consider the set of numbers a, 2a, 3a, ..., na where a and n are positive integers.

(a) Show that the expression for the mean of this set is.

(b) Let a = 4. Find the minimum value of n for which the sum of these numbers

exceeds its mean by more than 100.