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Magazine Problem 33
Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $$2+2^{2}+2^{3}+\cdots+2^{11}$$
Problem 33
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 12 terms of the geometric sequence: \(2,6,18,54 \ldots\)
Problem 33
Write a formula for the general term (the nth term of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20th term of the sequence $$a_{1}=4, d=-0.3$$
Problem 33
Write the first three terms in each binomial expansion, expressing the result in simplified form. $$(x-2 y)^{10}$$
Problem 34
Write a formula for the general term (the nth term of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20th term of the sequence $$a_{1}=5, d=-0.2$$
Problem 34
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 12 terms of the geometric sequence: \(3,6,12,24, \dots\)
Problem 34
Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $$5+5^{2}+5^{3}+\dots+5^{12}$$
Problem 34
Write the first three terms in each binomial expansion, expressing the result in simplified form. $$(x-2 y)^{9}$$
Problem 35
Write the first three terms in each binomial expansion, expressing the result in simplified form. $$\left(x^{2}+1\right)^{16}$$
Problem 35
Write a formula for the general term (the nth term of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20th term of the sequence Find the sum of the first 20 terms of the arithmetic sequence: \(4,10,16,22, \ldots\)
