Question

find the 99 th term of the series :31/4,19/2,45/4

Answer 1

The difference between 2 and 7 is 5

The difference between 7 and 14 is 7

The difference between 14 and 23 is 9

The difference between 23 and 34 is 11

5,7,9,11 are in AP with a difference of 2

Therefore the next term is with the difference of 2 [11 + 2 = 13}

The next term is 34 + 13 = 47

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OTHER ANSWERS



Krusna Balar, studied at Fountainhead School (2019)

Answered Apr 9 2017

The first level of differences are 5,7,9,11 and so on

The second level of differences is 2,2,2,2… [there can’t be a third level of differences as all the second level of differences are the same]

Now, given that there are two levels of differences, we can infer that the equation that represents this sequence will be quadratic [say there were three levels of differences, then it would have been a cubic equation]

KEY:

U - term

n - term no. [variable]

a,b,c - constants

U[n] = an2n2 + bn +c

In a sequence with two levels of 

Answer 2

AP: 31/4, 19/2, 45/4
d=-7/4
a=31/4
99th term =a+98d
=31/4+98*(-7/4)
=31/4-686/4
=-655/4