Question

find the average of 45 natural numbers starting from 454

Answer 1

Let's consider an AP consisting of 45 terms with first term 454 and common difference 1.

$T_{45} = 454 + 44 \times 1 \\ \\ = 454 + 44 = 498$

$Average = \frac{T_1 + T_{45}}{2} \\ \\ = \frac{454 + 498}{2} = \frac{952}{2} = 476 \\ \\ OR \\ \\ Average = T_{\frac{45 + 1}{2}} \\ \\ = T_{\frac{46}{2}} \\ \\ = T_{23} \\ \\ = 454 + 22 \times 1 \\ \\ 454 + 22 = 476$

∴ 476 is the average.

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