The Nth Term Of An AP

Derive and apply the general formula for the nth term of an AP.

6 lessons

Preview · progress not saved — Chapter 1 is free

f6eb0411...

content

Deriving the nth Term

Explain how Reena's salary leads to the a_n formula.

Real-World Patterns

Imagine you just got a new job with a starting salary of ₹ 8000 per month. Every year, you receive a guaranteed annual increment of ₹ 500.

Your salary for the 1st, 2nd, and 3rd years will be: 8000, 8500, 9000, . . .

If you want to know your salary for your 15th year, calculating it year-by-year would take too long. Let's find a faster way.

1 / 3

e4ec9ee0...

IMAGE

The nth Term Pattern

A visual mapping of the terms (a1, a2, a3) to their formulas.

bold editorial infographic, clean data-forward design, high-contrast color blocks, elegant typography hierarchy, geometr…

acd8be9b...

html

The General Term Formula

Formula for a_n.

The General Term Formula

a_{n} = a + (n - 1) d

a_{n}

The nth term (the value you are trying to find)

a

The first term (the starting value of the AP)

n

The position of the term (Must be a positive integer)

d

The common difference between consecutive terms

f6f94cce...

content

Finding a Specific Term

Example 3: Finding the 10th term.

Example 3: Finding a Specific Term

Problem: Find the 10th term of the AP: $2, 7, 12, \dots$

First, we extract our known values from the sequence:

First term, $a = 2$
Common difference, $d = 7 - 2 = 5$
Position, $n = 10$

1 / 4

2b0beee6...

reading

Practicing the Formula

Faded practice for finding a term.

0 of 3 blanks filled

Let's find the 30th term of the AP: $10, 7, 4, \dots$

First, identify the starting value: $a = 10$ . Next, calculate the common difference by subtracting the first term from the second: $d = 7 - 10 =$ . We want to find the 30th term, so $n = 30$ .

Using the formula $a_n = a + (n-1)d$ , substitute the values: $a_{30} = 10 + (30 - 1)($ $)$ . Solving inside the parentheses gives us $a_{30} = 10 + ($ $)(-3)$ . Multiplying first, $29 \times -3 = -87$ . Finally, $10 + (-87) = -77$ .

6ea7f455...

quiz

Order of Operations Check

Ensure n-1 is calculated correctly.

1 / 5

In the formula $a_n = 5 + (12-1)(-3)$ , what is the mathematically correct next step to solve?

← previousIntroducing Arithmetic Progressions next →Applications Of The Nth Term

content

Finding a Specific Term

Example 3: Finding the 10th term.

Example 3: Finding a Specific Term

Problem: Find the 10th term of the AP: $2, 7, 12, \dots$

First, we extract our known values from the sequence:

First term, $a = 2$
Common difference, $d = 7 - 2 = 5$
Position, $n = 10$

1 / 4

reading

Practicing the Formula

Faded practice for finding a term.

0 of 3 blanks filled

Let's find the 30th term of the AP: $10, 7, 4, \dots$

First, identify the starting value: $a = 10$ . Next, calculate the common difference by subtracting the first term from the second: $d = 7 - 10 =$ . We want to find the 30th term, so $n = 30$ .

quiz

Order of Operations Check

Ensure n-1 is calculated correctly.

1 / 5

In the formula $a_n = 5 + (12-1)(-3)$ , what is the mathematically correct next step to solve?