Completely the series.. 3,5,7,11,17,27,43,_,_,179,_
Answers
hey mate.
3+5-1 =7
5+7=1=11
like wise
27+43-1=69
43+69-1=111
69+111-1=179
111+179-1=289
Hope this helps.....
Answer:
3, 5, 7, 11, 17, 27, 43, 69, 111, 179, 289.
Step-by-step explanation:
The given numbers are 3, 5, 7, 11, 17, 27, 43, __, __, 179, __
Method I:
From the series, we can clearly figure out the relation:
3 + 5 - 1 = 7
7 + 5 - 1 = 11
11 + 7 - 1 = 17
17 + 11 - 1 = 27
It means that every number is obtained by adding previous two numbers and subtracting 1 from it.
Similarly, we get
27 + 17 - 1 = 43
43 + 27 - 1 = 69
69 + 43 - 1 = 111
111 + 69 - 1 = 179
179 + 111 - 1 = 289
Hence, the completed series is 3, 5, 7, 11, 17, 27, 43, 69, 111, 179, 289.
Method II:
Here, first of all we will write the differences between the given number.
5 - 3 = 2
7 - 5 = 2
11 - 7 = 4
17 - 11 = 6
27 - 17 = 10
43 - 27 = 16
Now, we can see clearly from above that every number is obtained by increasing the previous number with a factor of addition of the previous two differences. For example 11 is obtained by adding 7 and the addition of the previous two differences (2 + 2 = 4).
5 - 3 = 2
7 - 5 = 2 = 2 + 0
11 - 7 = 4 = 2 + 2
17 - 11 = 6 = 4 + 2
27 - 17 = 10 = 6 + 4
43 - 27 = 16 = 10 + 6
Accordingly, the next difference will be 16 + 10 = 26
Next number = 43 + 26 = 69
Next difference = 26+16 = 42
Next number = 69 + 42 = 111
Next difference = 42 + 26 = 68
Next number = 111+88 = 179 (already given)
Last difference = 68 + 42 = 110
Last number = 179 + 110 = 289
Hence, the completed series is 3, 5, 7, 11, 17, 27, 43, 69, 111, 179, 289.
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