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### Question

There is a sequence of 60 consecutive odd numbers. The average of first 18 of them is 78. What is the average of all the 60 numbers?

**A**

120.

**B**

121.

**C**

119.

**D**

118.

**Soln.**

**Ans: a**

The consecutive odd numbers form an AP with a common difference of 2. If the first term is a, then the average of first n terms of this AP is ${a + (a + (n-1) × 2)}/2$ which is = a + n-1. We are given the average of first 18 terms as 78. So a + 18 - 1 = 78, which gives a = 61. The average of first 60 terms would be a + 60 - 1 = 61 + 60 - 1 = 120.