Here is a cool sequence.
1,10,101,1020,10301,______,_______...
What numbers go in the two blanks?
First Step: The first number is 1, so we leave it as it is and since there is no number before that, we take it as 0.
Second Step: Multiply 1 (the first term) by 10 and add 0 to obtain the second term as 10.
Third Step: Multiply 10 (the second term) by 10 and add 1 (the first term) to obtain the third term as 101.
Fourth Step: Multiply 101 (the third term) by 10 and add 10 (the second term) to obtain the fourth term as 1020.
Fifth Step: Multiply 1020 (the fourth term) by 10 and add 101 (the third term) to obtain the fifth term as 10301.
Sixth Step: Multiply 10301 (the fifth term) by 10 and add 1020 (the fourth term) to obtain the sixth term as 104030.
Seventh Step: Multiply 104030 (the sixth term) by 10 and add 10301 (the fifth term) to obtain the seventh term as 1050601.
So, the general rule is given by:
'N'th Term = 10 times (N-1)st Term added to (N-2)nd Term.
Solution
