In the letter arrangement ABBBCCCCCDDDDDDD...... what will be letter at the place 145 ?

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18 Jan 2022 Sequence & Series

In the letter arrangement ABBBCCCCCDDDDDDD...... what will be letter at the place 145 ?

OPtion

1) K
2) M
3) L
4) J
5) N
6) P
7) O
8) I
9) Q
10) None of these

Solution

We can observe that, count of the letters forms the pattern like 1A, 3B, 5C, 7D, ..... which is in A.P. with difference of 2.
Now to get the 145th letter, we can find the sum of an A.P. for how many terms it gives sum=145
Sum of A.P. = (n/2)[2a + (n-1)d], where n=Number of terms, a=First term, d=Difference
145 = (n/2)[2*1 + (n-1)*2]
n^2 = 145
12 < n < 13
Thus, for 'n' we get the value more than 12 but less than 13, so 13th letter 'M' will be at 145th position in the series.

Correct Option: 2 Best Solution (3)

Arneet Singh   2 years AGO

sum of odd digits is square number and square root of 144 is 12 and alphabet at 12 is L so the position of 145 will be M

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Varun   2 years AGO

A ends at 1
B ends at 4
C ends at 9
.
.
12th letter ends at 144
13th letter M is from 145 to 169
=> Option (2)

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somya singh   2 years AGO

1+3+5+...=145
n*n=144
n=12
at 145 it would be 12+1 element =M

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