Find number of digits 1025th terms of the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,........ ?

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Filo · Accepted Answer

The given sequence is 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,....The sequence is composed by powers of 2 and repeated 2n times.We have,20=1 and 1 appears one time.21=2 and 2 appears twice.22=4 and 4 appears four times.23=8 and 8 appears eight times.So, the next number will be the next power of 2 and it will appear 2n times.also, the first 1 is in first position, the first 2 is in second position, the first 4 is in fourth position and so on.So, there is one 1, starting from position 1there are two 2s, starting from position 2there are four 4s, starting from position 4there are eight 8s, starting from position 8....there are one thousand and twenty four 1024s, starting from position 1024So, the 1025th number is 1024.

Question Text	Find number of digits $102 5^{t h}$ terms of the sequence $1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, ........$ ?
Answer Type	Text solution:1
Upvotes	150

Find number of digits $102 5^{t h}$ terms of the sequence $1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, ........$ ?

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