how many digits are there in the 10 th term of the sequence 1,23,456,78910...........
Answers
Step-by-step explanation:
In the sequence of sets {1}, {2,3}, {4,5,6,} ,{7,8,9,10}…and so on. What is the sum of elements in the 50th set?
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1st set = 1
2nd set = 2,3
3rd set = 4,5,6
you’ll notice that nth set has n elements, starts with the number which is 1+sum of 1st n-1 naturnal numbers and ends with sum of 1st n natural numbers.
So, for each set, we can determine that it’s an AP, with common difference as 1, first term as 1 + (n*(n-1)/2) [Sum upto n-1 natural nos.] and last term as n*(n+1)/2
The sum of AP can be written as n/2(a+l) where a is the first term, and l is the last term. 6
So, we have the sum of the elements of the nth set as:
(n(n-1)/2 + n(n+1)/2 + 1)*(n/2)
((n/2)*(n-1+n+1) + 1)*(n/2)
((n/2)*(2n) + 1)*(n/2)
(n^2 + 1)*n/2
(n^3 + n)/2.
So the sum of the 50th set is (50^3 + 50)/2 = 125050/2 = 62525