Exam 9: Progressions and the Binomial Theorem

For the problems below find the sum of the first $\mathrm{n}$ terms. - $a=3, r=\frac{1}{2}, n=4$

For the problems below find the sum of the first $\mathrm{n}$ terms. - $12,7,2, \ldots, n=17$

For the problems below, expand each binomial using the binomial theorem. - $(2 \mathrm{x}-5)^{6}$

For the problems below, find the sum of the infinite geometric series, if possible. - $15+3+\frac{3}{5}+\ldots+15\left(\frac{1}{5}\right) \mathrm{n}-1+\ldots$

For the problems below find the sum of the first $\mathrm{n}$ terms. - $a=3, \ell=23, n=6$

For the problems below find the nth term of the arithmetic progression. - $5,8,11, \ldots, n=7$

For the problems below find the nth term of the arithmetic progression. - $7,4.5,2, \ldots,=19$

Find the sum of the first 27 terms in an arithmetic progression where the first term is 32 and the 27 th term is - 83 .

For the problems below, find the indicated term of each binomial expansion. - $(5 x-2 y)^{7}$ fourth term

For the problems below, find the sum of the infinite geometric series, if possible. - $12+2+\frac{1}{3}+\ldots+12\left(\frac{1}{6}\right) \mathrm{n}-1+\ldots$