Find the 68th term of the arithmetic sequence – Delving into the realm of arithmetic sequences, we embark on a journey to uncover the secrets of finding the 68th term. This guide will provide a comprehensive understanding of the concept, empowering you to navigate the intricacies of this mathematical progression with ease.
Arithmetic sequences, characterized by their constant difference between consecutive terms, form the cornerstone of this exploration. We will unravel the formula that governs these sequences and demonstrate its application in determining the elusive 68th term.
Finding the 68th Term of an Arithmetic Sequence
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is the same. This difference is known as the common difference, denoted by d. The first term of an arithmetic sequence is denoted by a.
Identifying the Formula
The nth term of an arithmetic sequence is given by the formula:
an = a + (n
- 1)
- d
where:
- an is the nth term
- a is the first term
- n is the term number
- d is the common difference
Finding the 68th Term
To find the 68th term of an arithmetic sequence, we simply substitute n = 68 into the formula:
a68 = a + (68
- 1)
- d
Simplifying this expression, we get:
a68 = a + 67
d
Illustrative Examples, Find the 68th term of the arithmetic sequence
Consider the following arithmetic sequence:
| n | a | d | an |
|---|---|---|---|
| 1 | 5 | 3 | 5 |
| 2 | 8 | 3 | 8 |
| 3 | 11 | 3 | 11 |
| … | … | … | … |
| 68 | 5 | 3 | 209 |
To find the 68th term of this sequence, we substitute n = 68 into the formula:
a68 = 5 + (68
- 1)
- 3 = 209
Therefore, the 68th term of this arithmetic sequence is 209.
Step-by-Step Procedure
- Identify the first term (a) and common difference (d) of the arithmetic sequence.
- Substitute n = 68 into the formula: a68 = a + (68
- 1)
- d
- Simplify the expression to find the 68th term.
FAQ: Find The 68th Term Of The Arithmetic Sequence
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant.
How do I find the 68th term of an arithmetic sequence?
To find the 68th term of an arithmetic sequence, use the formula an = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number.
What is the formula for the nth term of an arithmetic sequence?
The formula for the nth term of an arithmetic sequence is an = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number.
