First slide

Arithmetic progression

Question

If A denotes the property that two elements of A = {1, 5, 9, 13 …, 1093} add up to 1094, then the maximum number of elements in A can be

Moderate

A

126
B

136
C

137
D

138

Solution

Since the elements in A are in A.P., therefore, the number of elements in $A = \frac{1093 - 1}{4} + 1 = 274$ .
Since, sum of equidistant terms in A.P. is equal to the sum of first and last term = 1 + 1093 = 1094.
$\Rightarrow$ maximum number of elements in A, that add up to 1094 $= \frac{274}{2} = 137$ .

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