Exam 10: Radicals, Radical Functions, and Rational Exponents

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a 17 when a1 = -4 , d = - 1 .

Find the common ratio for the geometric sequence. - $\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \frac { 3 } { 1024 } , \ldots$

Write out the first three terms and the last term of the arithmetic sequence. - $\sum _ { i = 1 } ^ { 60 } - 5 i$

Find the indicated sum. - $\sum _ { i = 1 } ^ { 4 } \left( - \frac { 1 } { 3 } \right) ^ { i }$

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. - $a _ { 1 } = 9 ; r = 2$

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a11 when a1 = 20, d = -6.

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. - $a _ { 1 } = - 2 ; r = 4$

Find the indicated sum. - $\sum _ { i = 1 } ^ { 5 } ( i - 7 )$

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d. -a1 = -36; d = 9

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d. -a1 = 18; d = -4

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. - $a _ { 1 } = 7 ; r = \frac { 1 } { 4 }$

Find the common ratio for the geometric sequence. -16, 8, 4, 2, 1, . . .

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first 70 terms of the arithmetic sequence: 1, 8, 15, 22, . . . .

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - $( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)$

Solve the problem. -The bar graph below shows a company's yearly profits from 2003 to 2011. Let an represent the company's profit, in millions, in year n, where n = 1 corresponds to 2003, n = 2 corresponds to 2004, and so on. $\text { Find } \sum _ { i = 4 } ^ { 9 } a _ { i }$

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a 32 when a1 = -3 , d = 3 .

Find the common ratio for the geometric sequence. - $\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 } , \ldots$

Write the first four terms of the sequence whose general term is given. - $\mathrm { a } _ { \mathrm { n } } = ( - 1 ) ^ { \mathrm { n } + 1 } ( \mathrm { n } + 7 )$

Solve the problem. -The population of a town is increasing by 400 inhabitants each year. If its current population is 29,089 and this trend continues, what would its population be in 8 years?

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence. - $a _ { 1 } = - 7 , d = 0.5$