91Ó°ÊÓ

Finding a Term in a Binomial Expansion In Exercises \(45-52,\) find the specified \(n\) th term in the expansion of the binomial. $$(4 x+3 y)^{9}, \quad n=8$$

In Exercises \(49-52,\) evaluate \(_{n} C_{r}\) using the formula from this section. $$_{5} C_{2}$$

Sum of a Finite Arithmetic Sequence In Exercises \(47 - 52 ,\) find the sum of the finite arithmetic sequence. $$ \- 5 + ( - 3 ) + ( - 1 ) + 1 + 3 + 5 $$

Writing the Terms of a Recursive Sequence In Exercises \(49-52\) , write the first five terms of the sequence defined recursively. $$ a_{1}=3, \quad a_{k+1}=2\left(a_{k}-1\right) $$

In Exercises \(49-52,\) evaluate \(_{n} C_{r}\) using the formula from this section. $$_{6} C_{3}$$

Finding a Term in a Binomial Expansion In Exercises \(45-52,\) find the specified \(n\) th term in the expansion of the binomial. $$(5 a+6 b)^{5}, \quad n=5$$

Finding a Sum In Exercises \(45-54\) , find the sum using the formulas for the sums of powers of integers. $$\sum_{n=1}^{8} n^{5}$$

Sum of a Finite Arithmetic Sequence In Exercises \(47 - 52 ,\) find the sum of the finite arithmetic sequence. Sum of the first 100 positive odd integers

Writing the Terms of a Recursive Sequence In Exercises \(49-52\) , write the first five terms of the sequence defined recursively. $$ a_{0}=1, a_{1}=2, \quad a_{k}=a_{k-2}+\frac{1}{2} a_{k-1} $$

In Exercises \(49-52,\) evaluate \(_{n} C_{r}\) using the formula from this section. $$_{4} C_{1}$$