Question

What is the average of the first 25 Multiple of 9 ?​

Answer 1

Answer:

What is the average of the first 25 multiples of 5?

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Method 1: The average = 5(1+25)/2 = 5*13 = 65.

Method 2. Sum of 25 terms of an Ap whose first term is 5 and common difference = 5 is

S25 = (25/2)[2*5 + (25–1)*5]

= (25/2)[10+24*5]

= (25/2)[10+120]

= 25*130/2

= 1625

So average of the 25 terms is 1625/25 = 65.

Method 3: Among 25 terms, the middle term will be the 13th term from either end and it will be the average of the whole series. The 13th term is 5x13 = 65.

So the average of the 25 terms which are multiples of 5 is 65.

Step-by-step explanation:

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Answer 2

Question ::-

What is the average of the first 25 Multiple of 9 ?

Solution ::-

1. First , take 25 multiple of 9 .

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225.

2. Add all the 25 first multiple of 9.

= 9 + 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81 + 90 + 99 + 108 + 117 + 126 + 135 + 144 + 153 + 162 + 171 + 180 + 189 + 198 + 207 + 216 + 225.

= 2925

3. Divide the sum by 25, as their are first 25 multiple of 9.

= $\dfrac{2925}{25}$

= 117 .

Hence, average of first 25 multiple of 9 is 117