What is the next term of the series 8, 14, 32, 86.

Expert Answers
pohnpei397 eNotes educator| Certified Educator

I believe that the next number in this sequence is going to be 248.

The way that I get this is by noticing a pattern between the 4 numbers that you have given us.  In each case, the difference between one number and the next number in the series is found by multiplying the first number by 3 and then subtracting 10 from the total.  In other words, if the first number is x and the second is y, then y = 3x -10.

So 8*3 = 24 and 24 - 10 = 14.  14*3 = 42 and 42 - 10 = 32.

Following that pattern, 86*3 = 258 and 258 -10 - 248 so the next number in the sequence is 248.

hala718 eNotes educator| Certified Educator

8, 14, 32, 86, ....

a1= 8

a2= 8+ 6 *1 =14

a3= 8+ 6*4 = 32

a4= 8+ 6*13 = 86

We notice that the series 1 , 4, 13, ... is  a(n-1) *3 + 1

==> 13*3 + 1 = 40

==> a5 = 8 + 6*40 = 248

 

william1941 | Student

Take a look at the terms of the series 8, 14, 32, 86. They don’t appear to be in an A. P. or a G. P. We have to try to look at other ways to find the next term of the series.

To do that we start by subtracting each term of the series from the previous term.

We get:

86 - 32 = 54

32 - 14 = 18

14 - 8 = 6

Now we see that 6*3= 18 and 18*3= 54.

Therefore to find the next term of the series we should multiply 54*3 = 162 and add 86. We get 248.

Therefore the next term of the series is 248.

neela | Student

The given sequence is 8,14,32,86....

To find the 5th term:

The differencee  of the  consecutive terms are:

14-8 = 6

32-14 = 18 = 3times previous difference = 3*

86-32 = 54.= 3 times previous difference. 3*18.

Therefore the next term = 86 +3*54 = 86 +162 = 242.

The

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