Which term of the A.P. 100, 90, 80,........... is zero?*5th6th10th11th

The given sequence is an arithmetic progression (A.P.) where the first term (a) is 100 and the common difference (d) is -10.

We need to find the term which is zero. In an A.P., the nth term is given by the formula:

a_n = a + (n-1)*d

We can set a_n to 0 and solve for n:

0 = 100 + (n-1)*(-10)

Solving this equation will give us the term of the A.P. that is zero.

First, distribute the -10 inside the parenthesis:

0 = 100 - 10n + 10

Combine like terms:

0 = 110 - 10n

Rearrange the equation to solve for n:

10n = 110

Finally, divide both sides by 10 to solve for n:

n = 110 / 10

n = 11

So, the 11th term of the A.P. is zero.