Question

Find the next 3 numbers in the pattern 3.5, 13, 41.5, 127, , , .

Answer 1

3 next number in the given pattern: 3.5 , 13, 41.5, 127, _______, _________, ________ We have the first 4 given pattern, next is to find the next 3 consecutive numbers:
x = numbers we’re looking
g =given numbers

=> 3.5g + x = 13
=> 13g + x = 41.5
=> 41.5g + x = 127

Now, let’s remove the decimals, multiply by 2
=> 2(3.5) + 2x = 2(13)
=> 7 + 2x = 26

=> 2 (13) + 2x = 2(41.5)
=> 26 + 2x = 83

=> 2(41.5) + 2x = 2(127)
=>83 + 2x = 247

Now, we already have whole numbers. Next is to solve the value of x’s and g’s
2x = 26-7
26 + 26 = 7 = 83
19 + 26 = 83
19 = 57
g = 3

2x = 26 -7
2x = 26 – 7 (3)
2x = 26 – 21
2x = 5
x = 2.5

Now, let’s find the next 3 consecutive numbers
=> 127 (3) + 2.5 = 383.5
=> 383.5 (3) + 2.5 = 1153
=> 1153 (3) + 2.5 = 3461.5

The next 3 numbers are 383.5, 1153, 3461.5

Answer 2

The correct answer is:

383.5 , 1153 , and 3461.5

Explanation:

We first find the first differences between terms. The difference between 13 and 3.5 is 9.5; the difference between 41.5 and 13 is 28.5; and the difference between 127 and 41.5 is 85.5. There is no noticeable pattern here, so we move on to the second differences.

For the second differences, the difference between 9.5 and 28.5 is 19; and the difference between 28.5 and 85.5 is 57. To get from 19 to 57 we multiply by 3, so this is the pattern we will begin with. The next second differences will be 57(3) = 171; 171(3) = 513; and 513(3) = 1539.

We add these second differences to the first differences: 85.5+171 = 256.5; 256.5 + 513 = 769.5; and 769.5 + 1539 = 2308.5.

Lastly, we add the first differences to the terms to find the next terms: 127+256.5 = 383.5; 383.5+769.5 = 1153; and 1153+2308.5 = 3461.5