Number sequences involving decimals

Learning Objectives Identify if a sequence with decimal terms is arithmetic, geometric, or neither. Calculate the common difference or common ratio for sequences involving decimals. Write the explicit formula for the nth term of an arithmetic or geometric sequence with decimal terms. Use the explicit formula to find the value of a specific term in a sequence involving decimals. Solve problems by finding the position of a given decimal term within a sequence. Distinguish between the term number (n) and the term's value (a_n) in decimal sequences. If a leaky faucet drips 1.5 mL of water the first minute, 2.25 mL the second, and 3.0 mL the third, how much will it drip in the tenth minute? 💧 This tutorial explores number sequences where the terms are decimals. You will le...

TermDefinitionExample SequenceAn ordered list of numbers, called terms, that follow a specific pattern or rule.0.2, 0.4, 0.6, 0.8, ... Term (a_n)An individual number in a sequence. The notation 'a_n' refers to the term in the nth position.In the sequence 5.5, 6.0, 6.5, ..., the third term (a_3) is 6.5. Arithmetic SequenceA sequence where the difference between consecutive terms is constant. This constant value is the common difference (d).10.8, 10.5, 10.2, 9.9, ... (The common difference is -0.3). Common Difference (d)The fixed amount added to each term to get the next term in an arithmetic sequence. It can be positive, negative, or zero.For the sequence 1.25, 1.50, 1.75, ..., the common difference is d = 1.50 - 1.25 = 0.25. Geometric SequenceA sequence where the ratio between c...

Arithmetic Sequence Formula a_n = a_1 + (n-1)d Use this formula to find the value of the nth term (a_n) of an arithmetic sequence. You need the first term (a_1), the term number you want to find (n), and the common difference (d). Geometric Sequence Formula a_n = a_1 * r^(n-1) Use this formula to find the value of the nth term (a_n) of a geometric sequence. You need the first term (a_1), the term number you want to find (n), and the common ratio (r).