Exam 10: Radicals, Radical Functions, and Rational Exponents

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first four terms of the arithmetic sequence: -3, -15, -27, . . . .

Find the indicated sum. - $\sum _ { i = 4 } ^ { 10 } 12$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { 3 ^ { n } } { ( n + 3 ) ! }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { n + 8 }$

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. - $a _ { 1 } = 6 , r = - 10$

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - $11 + 14 + 17 + 20 + \ldots + 35$

Find the indicated sum. - $\sum _ { k = 2 } ^ { 4 } k ( k + 3 )$

Find the common ratio for the geometric sequence. - $4 , - 12,36 , - 108,324 , \ldots$

Solve the problem. -A theater has 30 rows with 26 seats in the first row, 30 in the second row, 34 in the third row, and so forth. How many seats are in the theater?

Find the indicated sum. - $\sum _ { i = 3 } ^ { 6 } ( 4 i - 4 )$

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

Write the first four terms of the sequence whose general term is given. - $a _ { n } = 5 n$

Find the common ratio for the geometric sequence. - $7 , - 0.7,0.07 , - 0.007 , \ldots$

Write the first four terms of the sequence whose general term is given. - $\mathrm { a } _ { \mathrm { n } } = ( - 1 ) ^ { \mathrm { n } } ( \mathrm { n } + 4 )$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \left( - \frac { 2 } { 5 } \right) ^ { n }$

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - $3 + \frac { 7 } { 2 } + 4 + \frac { 9 } { 2 } + \ldots + \frac { 15 } { 2 }$

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { i = 1 } ^ { 25 } ( 2 i - 7 )$

Find the common ratio for the geometric sequence. - $2 , \frac { 6 } { 5 } , \frac { 18 } { 25 } , \frac { 54 } { 125 } , \ldots$

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 a8 when a1 = -8 , d = -5 .

Find the common difference for the arithmetic sequence. -3, 5, 7, 9, . . .