Arithmetic Sequences Calculator

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Example

Created on 2024-06-20Asked by Noah Anderson (Solvelet student)

Find the 10th term of the arithmetic sequence where the first term is 3 and the common difference is 5.

Solution

Step 1: Identify the first term (

a_1

) and the common difference (

d

). The first term is 3 and the common difference is 5. Step 2: Use the formula for the

n

th term of an arithmetic sequence:

a_n = a_1 + (n-1)d.

Step 3: Substitute

a_1 = 3

d = 5

, and

n = 10

into the formula:

a_{10} = 3 + (10-1) \cdot 5 = 3 + 9 \cdot 5 = 3 + 45 = 48.

Step 4: Conclusion. The 10th term of the arithmetic sequence is 48. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Madison Brown on Solvelet

1. Find the 20th term of the arithmetic series:

3, 7, 11, 15, \ldots

2. Find the sum of the first 10 terms of the arithmetic sequence:

2, 5, 8, 11, \ldots

DefinitionArithmetic sequence is a sequence of numbers for which the difference between any two successive numbers is always the same. It is usually denoted by the formula. Here, the first term is, is the common difference, and is the term number. Mathematicians use arithmetic sequences to describe the linear growth of sequences, while in finance, they can be used to describe the interest on deposits or loans. Frequently used in the calculation of sums of series, prediction of the future values, and analysis of algorithms. For instance: 3,7,11,15,…This is an arithmetic sequence with a first term a1=3 and a constant difference d=4. This is an arithmetic sequence and the formula we will use to find this, is an=3+(n−1)4.

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