91Ó°ÊÓ

Find the sum of all the four-digit positive integers.

Consider an arithmetic sequence with first term b and difference \(d\) between consecutive terms. (a) Write the sequence using the three-dot notation, giving the first four terms of the sequence. (b) Give the \(100^{\text {th }}\) term of the sequence. \(b=8, d=-5\)

Find the smallest integer \(n\) such that \(0.9^{n}<10^{-200}\).

Find the sum of all the four-digit odd positive integers.

Consider an arithmetic sequence with first term b and difference \(d\) between consecutive terms. (a) Write the sequence using the three-dot notation, giving the first four terms of the sequence. (b) Give the \(100^{\text {th }}\) term of the sequence. \(b=0, d=\frac{1}{3}\)

Find the sum of all the four-digit positive integers that are evenly divisible by 5

Consider an arithmetic sequence with first term b and difference \(d\) between consecutive terms. (a) Write the sequence using the three-dot notation, giving the first four terms of the sequence. (b) Give the \(100^{\text {th }}\) term of the sequence. \(b=-1, d=\frac{3}{2}\)

In the decimal expansion of \(0.9^{9999}\), how many zeros follow the decimal point before the first nonzero digit?

In Exercises 15-24, evaluate the geometric series. \(1+3+9+\cdots+3^{200}\)

Consider a geometric sequence with first term \(b\) and ratio \(r\) of consecutive terms. (a) Write the sequence using the three-dot notation, giving the first four terms. (b) Give the \(100^{\text {th }}\) term of the sequence. \(b=1, r=5\)