11, 22,33 what is fomula in the sequence
Answers
Few things which are common in the given sequence, are given below.
Method 1 : -
11 / 22 = 11 x 1 / 11 x 2
22 / 33 = 11 x 2 / 11 x 3
According to this, other term will 11 x 3 / 11 / x 4 i.e. 33 / 44 .
So, ( denominator of the previous term ) / ( 11 x ( co efficient of 11 in denominator + 1 ) will satisfy all the terms of this sequence.
In this, numerator is 33( given term & 3rd term ) and denominator is the term after 33( 4th term ) i.e. 11 x ( 3 + 1 ) = 11 x 4 = 44
Method 2 : -
11 is at 1st place, 11 is multiplied by 1
22 is at 2nd place, 11 is multiplied by 2
33 is at 3rd place, 11 is multiplied by 3
Therefore, next will be, 4th term = 11 x 4 = 44
Thus, we can say that sequence is based on 11 x ( term )
Method 3 : - ( AP )
Given sequence = 11 , 22 , 33....
Common difference = 22 - 11 = 33 - 22 = 11
From the identities of arithmetic progressions,
aₓ = a + ( n - 1 )d
From the question, 11 + ( n - 1 )11
⇒ 11 + 11n - 11
⇒ 11 - 11 + 11n
⇒ 11 n
From these we can say that the sequence is based on the product of 11 and the number of term.