91Ó°ÊÓ

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, \(a_{1},\) and common ratio, \(r .\) Find \(a_{6}\) when \(a_{1}=6400, r=-\frac{1}{2}\).

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$\left(2 x^{3}-1\right)^{4}$$

Use the formula for the general term (the nill term of an arithmetic sequence to find the indicated term of each sequence with the given first term, \(a_{1},\) and common difference, \(d\) Find \(a_{200}\) when \(a_{1}=-40, d=5\)

Find each indicated sum. $$\sum_{k=1}^{5} k(k+4)$$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, \(a_{1},\) and common ratio, \(r .\) Find \(a_{6}\) when \(a_{1}=8000, r=-\frac{1}{2}\).

Find each indicated sum. $$\sum_{k=1}^{4}(k-3)(k+2)$$

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$\left(2 x^{5}-1\right)^{4}$$

Use the formula for the general term (the nill term of an arithmetic sequence to find the indicated term of each sequence with the given first term, \(a_{1},\) and common difference, \(d\) Find \(a_{150}\) when \(a_{1}=-60, d=5\)

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, \(a_{1},\) and common ratio, \(r .\) Find \(a_{8}\) when \(a_{1}=1,000,000, r=0.1\).

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$(c+2)^{5}$$