Question

If 13 is the first triangular number which is the tenth one​

Answer 1

Answer:

As we know that the triangular numbers are

1,3,6,10,15,21,……….upto n terms.And also we have the nth term of this series {i.e. the nth triangular number} is {n (n+1)}/2 and if we want to find the 3rd triangular number then we put n=3,and we get the 3rd triangular number is 6, as given in the above series…

And now as your question that if 3 is the first triangular number then what is the 10th triangular number. So here if we consider that 3 is the first term(i.e. 1st triangular number) then the series will be 3,6,10,15,21,…………upto n terms.And here from the above series one term (1st term) has been neglected, then obviously the nth triangular number i.e[ {n(n+1)}/2 ] will be change and we will use (n-1) for n in the nth term and now the nth term is {n (n-1)}/2 and then to find the 10th term of this series {i.e. series of the triangular numbers } we will put n=10 and we will get the 10th triangular number is 45.