Find the missing number in the series.
20, 35, 60, 105, 190, _____
- A225
- B280
- C560
- D355
Solution & Step-by-step Explanation
Let's look at the differences between consecutive terms:
35−20=15
60−35=25
105−60=45
190−105=85
Now, let's look at the sequence of differences: 15, 25, 45, 85.
Let's see the pattern within these differences:
25−15=10
45−25=20
85−45=40
The differences between the differences are doubling each time (10×2=20, 20×2=40).
Following this rule, the next difference increment should be:
40×2=80
So, the next difference value added to the series will be:
85+80=165
Adding this to the last term of the main series:
Missing number=190+165=355
Alternative Method:
Let's analyze each term in relation to the previous term multiplied by 2:
20×2−5=40−5=35
35×2−10=70−10=60
60×2−15=120−15=105
105×2−20=210−20=190
Following this logic (×2−multiples of 5):
Missing number=190×2−25=380−25=355
Both methods lead to 355.
35−20=15
60−35=25
105−60=45
190−105=85
Now, let's look at the sequence of differences: 15, 25, 45, 85.
Let's see the pattern within these differences:
25−15=10
45−25=20
85−45=40
The differences between the differences are doubling each time (10×2=20, 20×2=40).
Following this rule, the next difference increment should be:
40×2=80
So, the next difference value added to the series will be:
85+80=165
Adding this to the last term of the main series:
Missing number=190+165=355
Alternative Method:
Let's analyze each term in relation to the previous term multiplied by 2:
20×2−5=40−5=35
35×2−10=70−10=60
60×2−15=120−15=105
105×2−20=210−20=190
Following this logic (×2−multiples of 5):
Missing number=190×2−25=380−25=355
Both methods lead to 355.