What is the next number of the following sequence 1,5,5,3,10,10,5,6,......

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02 Dec 2013 Sequence

What is the next number of the following sequence
1,5,5,3,10,10,5,6,......

OPtion

1) 8
2) 9
3) 10
4) 12
5) 14
6) 15
7) 18
8) 24
9) 25
10)None of these

Solution

1 = 1
1^2+2^2 = 1+4 = 5 = 5
1^2+2^2+3^2 = 1+4+9 = 14 = 1+4 = 5 (Sum of digit)
1^2+2^2+3^2+4^2 = 1+4+9+16 = 30 = 3+0 = 3
1^2+2^2+3^2+4^2+5^2 = 1+4+9+16+25 = 55 = 5+5 = 10
1^1+2^2............+6^2 = 1+4+...+36 = 55+36 = 91 = 9+1 = 10
1^2+2^2+............+7^2 = 1+4+.....+49 = 91+49 = 140 = 1+4+0 = 5
1^2+2^2+...............+8^2 = 1+4+.....+64 = 140+64 = 204 = 2+0+4 = 6
Similarly next
1^2+2^2+...................+9^2=1+4+......+81 = 204+81=285=2+8+5= 15
option 6)

Correct Option: 6 Best Solution (8)

Udhaya kumar   11 years AGO

1=1
1+4=5
1+4+9=14=5
1+4+9+16=30=3
1+4+9+16+25=55=10
1+4+9+16+25+36=91=10
1+4+9+16+25+36+49=140=5
1+4+9+16+25+36+49+64=204=6
1+4+9+16+25+36+49+64+81=285=15...........

Like? Yes (25) | No (3)  

jitendra   11 years AGO

because in sequence number increases by 5

Like? Yes (1) | No   

T.P.Vipin Krishna   11 years AGO

Multiples of five are repeating

Like? Yes (1) | No   

Ramanjaneyulu   11 years AGO

1 5 5 3 10 10 5 6 ? 7
(1+3) (3+5) (5+7)
4 8 12
4+1 8+2 12+3
5 10 15
->At first the sequence followd is 1,3,5,7
->add these conecutive 2 nums 1+3 3+5 5+7
->Add then 1,2,3 respectively to each of this result.

Like? Yes (1) | No   

Dr.Dipin Singh   11 years AGO

Sum of digits of
sigma (n^2)

Like? Yes (1) | No   

Koushik Pal   11 years AGO

3rd position number is 5
6th position number is 10
so, 9th position number is 15

Like? Yes (1) | No   

Dhinakaran   11 years AGO

it will splitted to two parts...

1--->5 , 5
3--->10 , 10 , 5
6--->15 , 15 , 10 , 5...
.
.
.

because the next number is 15

Like? Yes (1) | No (3)  

Gayathri   11 years AGO

next to 1 its 2- 5,next to 3 its 2-10,so next to 6 its 2-15

Like? Yes (1) | No (3)