Homeclass 10MathsArithmetic ProgressionsFirst Term

First Term

The first term of an Arithmetic Progression is the initial number or starting value of the sequence. It is typically denoted by the letter a or a1 and forms the foundation from which all subsequent terms are calculated.

Key Concepts

The first term establishes the starting point of the arithmetic sequence on a number line.
In the general form of an arithmetic progression represented as a, a+d, a+2d, the letter a stands for the first term.
Knowing just the first term and the common difference allows you to find any other term or the sum of the sequence.

Formula & Equation

an = a + (n - 1)d

an is the nth term, a is the first term, n is the position of the term, and d is the common difference.

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Common Misconceptions

Myth: The first term of an arithmetic progression must always be a positive whole number.
Fact: The first term can be any real number, which includes negative numbers, fractions, decimals, and even zero.

Real World Applications

If a taxi fare has a fixed base charge of Rs 50 and increases by Rs 10 for every additional kilometer, the base charge of Rs 50 represents the first term.
When starting a savings plan with an initial deposit of Rs 500 and adding Rs 50 each month, the initial Rs 500 is the first term.

Frequently Asked Questions

How do you find the first term of an AP if the general formula for the nth term is given?
You can find the first term by substituting n = 1 into the given nth term formula.
Can the first term and the common difference of an AP be the same value?
Yes, they can be the same. For example, in the sequence 3, 6, 9, 12, both the first term and the common difference are 3.

Keep Learning

Arithmetic ProgressionCommon DifferenceGeneral Form of an Arithmetic Progression