Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a_n = a_n-1 +3, a₁ = 4

Find each indicated sum. ${\sum }_{i=1}^{4}2i^2$

In Exercises 31–34, write the first five terms of each geometric sequence. a1 = 1/2, r = 1/2

Use mathematical induction to prove that each statement is true for every positive integer n. (ab)ⁿ = aⁿ bⁿ

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. ${\sum }_{i=1}^{10}5\cdot 2^i$

Write the first three terms in each binomial expansion, expressing the result in simplified form. (x - 2y)¹⁰

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

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a_n= a_n-1 -10, a₁ = 30

Write the first three terms in each binomial expansion, expressing the result in simplified form. (x² + 1)¹⁶

Find the sum of the first 20 terms of the arithmetic sequence: 4, 10, 16, 22,……….

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence. Find a₇ when a₁ = 2, r = 3

Find each indicated sum. ${\sum }_{i=1}^4{(-\frac{1}{2})}^i$

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.${\sum }_{i=1}^6{\left(\frac{1}{2}\right)}^{i+1}$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence. Find a(sub 6) when a(sub 1) = 16, r = 1/2

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence. Find a₅ when a₁ = -3, r = 2

Write the first three terms in each binomial expansion, expressing the result in simplified form. (y³ − 1)²⁰

Find each indicated sum. ${\sum }_{i=5}^{9}11$

Find the sum of the first 50 terms of the arithmetic sequence: -10, -6, -2, 2,....

Find the sum of each infinite geometric series. 1 + 1/3 + 1/9 + 1/27 + ...

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a(sub n) to find a(sub 8), the eighth term of the sequence. 1, 2, 4, 8, ...

Find the term indicated in each expansion. (2x + y)⁶; third term

Find the sum of each infinite geometric series. 3 + 3/4 + 3/4² + 3/4³ + ...

In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a king.

Find 1+2+3+4+...+ 100, the sum of the first 100 natural numbers.

Find each indicated sum. ${\sum }_{i=0}^4\frac{(-1{)}^i}{i!}$

In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a picture card.

Find the sum of the first 60 positive even integers.

Find the sum of the first 15 terms of the geometric sequence: 5, -15, 45, -135

Find the term indicated in each expansion. (x − 1)⁹; fifth term

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