Latest Elitmus Aptitude Question SOLUTION: 1 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 .........,sum of first 1230 terms of series.

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(#M40154088) ELITMUS Numerical Ability question Keep an EYE

1 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 .........,sum of first 1230 terms of series.

Asked In Elitmus dytort (8 years ago)

Solved sunil mehta Read Solution (7)

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Read Solution (7) :

sunil mehta  (8 years ago) Best Solution

We have to find the no. of 1's and no. of 2's in 1230 terms...
Lets take 1st two terms ... 1, 2
no. of 1's is 1 nd no. of 2's is 1 => (1+1)
1st 5 terms ... 1,2,1,2,2
=> (1+1)+(1+2)
1st 9 terms ... 1,2,1,2,2,1,2,2,2
=> (1+1)+(1+2)+(1+3)
=> (1+1+1)+(1+2+3)
3 + 3(3+1)/2
[Its of the form n + n(n+1)/2].
So in 1st n terms, no. of 1's is "n", no. of 2's is n(n+1)/2
So sum of 1st n terms ll be n*1 + n(n+1)
So for the 1230 terms,
n + n(n+1)/2
n=48
48 + 48*49/2 = 1224 and next 6 no. are 1+2+2+2+2+2 = 11
So total sum will be = 48*1 + 48*49 + 11 = 2411
Ans : 2411

Is this solution Helpfull? Yes (19) | No   

arpit srivastava  (7 years ago)

Group the no. As follows:

X= {1, 2+1, 2+2+1, 2+2+2+1, 2+2+2+2+1,…}

Now it gives you A.P. as follows:

Y= {1, 3, 5, 7, 9,…}

Number of terms contained in each Y is:

Z= {1, 2, 3, 4, 5…}

Given the sum to be found ulti 1230 terms but 1230 doesn't give you the exact number if you solve it by sum of n natural no.s formulae. So break 1230 into 1225+5.

Now find the value of n given the sum is 1225.

n(n+1)/2 = 1225

This gives n=49

Now use the sum of A.P. formulae in Y:

Sum= n[2a+(n-1)d]/2

Where n=49, a=1, d=2 we get:

Sum = 2401

Now this is the result for 1225 no.s

To get the result of 1230 no.s we need to add the next 5 numbers in the sequence (which starts with 2). So the next 5 terms are 2,2,2,2,2.

Therefore =2*5 = 10

Final result is 2401+10 = 2411

Is this solution Helpfull? Yes (11) | No   

manmohan  (8 years ago)

Start with making two series
1+1*2=3 terms 2
1+2*2=5. 3
1+3*2=7. 4
....
....
....
1+47*2=95. 48
1+48*2=97. 49

And last term
1+5*2=11. 6
Total sum= 48(3+97)/2+11=2411

Is this solution Helpfull? Yes (4) | No   

avinash jha  (8 years ago)

1 occuring at positions 1,3,6,10 & ......so on.it is of the format n*(n+1)/2. So now n*(n+1)/2=1230. Or n*(n+1)=2460. So putting n=49 in the equation we get no of occurrnce of 1. So remaing are digit 2.and the no. 2's are 1230-49=1189.this 1189 are the no. Of 2. So their sum will be 1189*2=2362.so total=sum of 2 + sum of 1= 2362+49=2411.

Is this solution Helpfull? Yes (3) | No (2)  

saketh  (8 years ago)

2313 is the answer

Is this solution Helpfull? Yes | No (2)  

Mithilesh Times  (8 years ago)

2411 is correct ans

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  (6 years ago)

Which book u r referring to solve this type of questions

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