1,2,2,4,4,4,8,8,8,8,.........find the 1000th term.

Dear aritra,

1,2,2,4,4,4,8,8,8,8........

above sequence can be written as

2⁰,2¹,2¹,2²,2²,2²,2³,2³,2³,2³,........    so we see that exponent of 2 and the n^th term is interrelated

exponent 0 is the first term 1 is 1 time

exponent 1 is the second term and the third term 2 is 2 times 

exponent 2 is the fourth fifth and sixth term  4 is 3 times

exponent n                                               2ⁿ   is n-1 times

to find out 1000th term  we have to find out in which range does it come so by n(n+1)/2

for n = 44 we get 990 so 1000 term we will get after it  the 1000 term would be 2^{44 is the thousndth term}

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