find this pattern: 10,40,90,61,52,63,94,46,18,100
and find the next 2 terms in the sequence
two circles C(O;a) and C'(H;b) tangent externally at A.Aline passing through A cuts circle (C) in B and circle (C') in E
To find the pattern in the given sequence, let's observe the differences between consecutive terms:
Difference between adjacent terms:
40 - 10 = 30
90 - 40 = 50
61 - 90 = -29
52 - 61 = -9
63 - 52 = 11
94 - 63 = 31
46 - 94 = -48
18 - 46 = -28
100 - 18 = 82
Now, let's analyze the differences further:
The differences between adjacent terms seem to be alternating between positive and negative values. Also, the magnitude of the differences is increasing pattern in this sequence.
Considering the first few differences:
30, 50, -29, -9, 11, 31
We can observe that:
30 + 50 = 80
-29 + (-9) = -38
11 + 31 = 42
So, there seems to be another pattern emerged with the differences:
80, -38, 42
Now, let's consider the second set of differences:
-38 + 42 = 4
We can see that the differences between the second set of differences are showing a constant value of 4.
Therefore, we can conclude that the pattern of this sequence is as follows:
Starting with 10, each term is obtained by adding the corresponding term number in the series to 10, and then adding the previous difference.
Now let's find the next 2 terms in the sequence:
- The 11th term would be obtained by adding 11 to 10 and adding the previous difference of 4:
10 + 11 + 4 = 25
- The 12th term would be obtained by adding 12 to 25 and adding the previous difference of 4:
25 + 12 + 4 = 41
So, the next two terms in the sequence are 25 and 41.