Question

Find the middle term(s) of even numbers from 50 to 500.
312,314
316,318
314, 316
318,320​

Answer 1

The set = 50,52,54,56,58,........,492,494,496,498,500

Number of terms = $\bold{(\frac{x_n-x_1}{d})+1}$

Here,

• $\bold{x_n=Last\:Term}$

• $\bold{x_1=First\:Term}$

• $\bold{d=Common\:Difference}$

Number of terms (n) = 225+1 = 226

Median = Average of n/2 and n/2 + 1

Here,

n/2 = 226/2 = 113th term

n/2 + 1 = 113 + 1 = 114th term

nth term = a+(n-1)d

113th term = 50+(112×2) = 50+224 = 274

114th term = 274 + 2 = 276

Therefore the terms are 274 and 276

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How to find middle term of even numbers

• First arrange the given numbers in ascending order

• If there are ’n’ even numbers,median is the average of n/2 and n/2+1 th values