Question

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Which category of category 4,9,14 19,.....................is 104 ?

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Answer 1

Hey!

As one of the solutions is solved using arithmetic progression. I want to give observance a try. :)

Thank you!


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Solution:

So the sequence flows as 4, 9, 14, 19,...

The trick is as follows:

From the first term 4,

⇒ 4 + 5 = 9
⇒ 9 + 5 = 14
⇒ 14 + 5 = 19
⇒ 19 + 5 = 24  and the series will goes on by adding the number 5 to the previously resulted number.

So, the resulted number - previous number will give the number to which 5 was added.

let it be x

x = 104 - 5
x = 99

So, the answer is 99. [the previous number to 104]

The series will be: 4,9,14,19,...,99,104


Solution through observance:

The series continues taking two numbers for every increment of ten as in [ for first 10, it posses two numbers (4,9) and for the second ten (14,19)] and goes on.

As the sequence reaches 99, the category will become 10x2 = 20th

The very next number to 99 is 104 with the increment of 1 category = 20+1 =21.

Therefore, the number 104 belongs to the 21th category.

Answer 2

Hey Mate

your answer is ---

Given, sequence is 4,9,14,19.......104

now, 9-4 = 5 , 14-9 = 5

so, the given sequence is an AP with first term a = 4 and common difference d =5

Let, n term of an AP is 104

therefore,

✔ Tn = a+(n-1)d

=> 104 = 4 + (n-1) 5

=> (n-1)5 = 100

=> n-1 = 100/5

=> n-1 = 20

=> n = 20+1

=> n = 21

Hence, 21th category of category 4,9,14 19,.....................is 104.

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