Others Maths Puzzle

The first two terms of a series are ‘a’ and ‘b’ respectively, (a, b > 0) and thereafter, every subsequent term is the average of the previous two terms. What is the 12th term of this series?

options

a--(171a + 341b)/512
b--(343a + 681b)/1024
c--(341a + 683b)/1024
d--(683a + 1365b)/2048

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Others Other Question
A googol is a large number equal to 10^100 but a googleplex is a still larger number equal to 1 followed by a googol zeroes. If you write 1 googleplex in base googol, how many zeroes will come at the end ?

1. 10^96
2.10^97
3. 10^98
4. 10^99
5. 10^100 There are three urns numbered 1, 2 and 3. Urn 1 has 2 black balls and 3 white balls. Urn 2 has 1 black ball and 2 white balls. Urn 3 has 2 black balls and 1 white ball. A person who is blindfolded, picks a ball from urn 1, puts it into urn 2, picks a ball from urn 2 and puts it into urn 3 and finally picks a ball from urn 3 and puts it into urn 1. What is the probability that at the end of round 1 all the urns have exactly the same composition as they originally started off with?
a)5/8
b)2/5
c)3/5
d)1/4
e)3/8