Arithmetic sequences with fractions

Learning Objectives Identify the first term and common difference in an arithmetic sequence involving fractions. Calculate the value of any term (the nth term) in an arithmetic sequence with fractions. Write an explicit formula for an arithmetic sequence with fractional terms. Calculate the sum of a finite number of terms in an arithmetic sequence with fractions. Determine the number of terms in a finite arithmetic sequence with a fractional common difference. Solve real-world problems modeled by arithmetic sequences involving rational numbers. Imagine a plant that grows exactly 3/4 of an inch every day. How tall would it be after 20 days? 🤔 This is an arithmetic sequence with fractions in action! This tutorial will guide you through arithmetic sequences where the terms or...

TermDefinitionExample Arithmetic SequenceA sequence of numbers where the difference between any two consecutive terms is constant.The sequence 1/2, 1, 3/2, 2, ... is an arithmetic sequence because you add 1/2 to each term to get the next. Term (a_n)A single number in a sequence. We use a_n to denote the nth term, where 'n' is the term's position.In the sequence 1/2, 1, 3/2, 2, ..., the third term is a_3 = 3/2. First Term (a_1)The starting number of a sequence.In the sequence 1/2, 1, 3/2, 2, ..., the first term is a_1 = 1/2. Common Difference (d)The constant amount added to each term to get the next term. It can be positive, negative, or a fraction.In the sequence 5/4, 1, 3/4, 1/2, ..., the common difference is d = -1/4. Rational NumberAny number that can be expressed as a f...

The nth Term Formula a_n = a_1 + (n-1)d Use this formula to find the value of any specific term (a_n) in a sequence if you know the first term (a_1), the common difference (d), and the term number (n). The Sum of a Finite Arithmetic Sequence S_n = n/2 * (a_1 + a_n) Use this formula to find the sum (S_n) of the first 'n' terms when you know the first term (a_1), the last term (a_n), and the number of terms (n). The Alternative Sum Formula S_n = n/2 * (2a_1 + (n-1)d) Use this formula to find the sum (S_n) of the first 'n' terms when you know the first term (a_1), the common difference (d), and the number of terms (n). It's useful when you don't know the last term.