Problems on Arithmetic Progression

Here we will learn how to solve different types of problems on arithmetic progression.


1. Show that the sequence 7, 11, 15, 19, 23, .........  is an Arithmetic Progression. Find its 27th term and the general term.

Solution:

First term of the given sequence = 7

Second term of the given sequence = 11

Third term of the given sequence = 15

Fourth term of the given sequence = 19

Fifth term of the given sequence = 23

Now, Second term - First term = 11 - 7 = 4

Third term - Second term = 15 - 11 = 4

Fourth term - Third term = 19 - 15 = 4

Fifth term – Fourth term = 23 - 19 = 4

Therefore, the given sequence is an Arithmetic Progress with the common difference 4.

We know that nth term of an Arithmetic Progress, whose first term is a and common difference is d is tn = a + (n - 1) × d.

Therefore, 27th term of the Arithmetic Progress = t27 = 7 + (27 - 1) × 4 = 7 + 26 × 4 = 7 + 104 = 111.

General term = nth term = an = a + (n - 1)d = 7 + (n - 1) × 4 = 7 + 4n - 4 = 4n + 3

 

2. The 5th term of an Arithmetic Progression is 16 and 13th term of an Arithmetic Progression is 28. Find the first term and common difference of the Arithmetic Progression.

Solution:

Let us assume that ‘a’ be the first term and ‘d’ be the common difference of the required Arithmetic Progression.

According to the problem,

5th term of an Arithmetic Progression is 16

i.e., 5th term = 16

⇒ a + (5 - 1)d = 16

⇒ a + 4d = 16 ................... (i)

and 13th term of an Arithmetic Progression is 28

i.e., 13th term = 28

⇒ a + (13 - 1)d = 28

⇒ a + 12d = 28 .................... (ii)

Now, subtract the equation (i) from (ii) we get,

8d = 12

⇒ d = \(\frac{12}{8}\)

⇒ d = \(\frac{3}{2}\)

Substitute the value of d = \(\frac{3}{2}\) in the equation (i) we get,

⇒ a + 4 × \(\frac{3}{2}\) = 16

⇒ a + 6 = 16

⇒ a = 16 - 6

⇒ a = 10

Therefore, the first term of the Arithmetic Progression is 10 and common difference of the Arithmetic Progression is \(\frac{3}{2}\).

Arithmetic Progression






11 and 12 Grade Math 

From Problems on Arithmetic Progression to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Subtraction of Decimals | Subtracting Decimals | Decimal Subtraction

    Apr 24, 25 03:25 PM

    Subtraction of Decimals
    We will discuss here about the subtraction of decimals. Decimals are subtracted in the same way as we subtract ordinary numbers. We arrange the digits in columns

    Read More

  2. How to Do Long Division? | Method | Steps | Examples | Worksheets |Ans

    Apr 24, 25 10:18 AM

    Long Division and Short Division Forms
    As we know that the division is to distribute a given value or quantity into groups having equal values. In long division, values at the individual place (Thousands, Hundreds, Tens, Ones) are dividend…

    Read More

  3. Division by Two-Digit Numbers | Knowledge of Estimation | Division

    Apr 24, 25 10:12 AM

    Divide 5-Digit by 2-Digit Number
    In division by two-digit numbers we will practice dividing two, three, four and five digits by two-digit numbers. Consider the following examples on division by two-digit numbers: Let us use our knowl…

    Read More

  4. Addition of Decimals | How to Add Decimals? | Adding Decimals|Addition

    Apr 24, 25 01:45 AM

    Addition of Decimals
    We will discuss here about the addition of decimals. Decimals are added in the same way as we add ordinary numbers. We arrange the digits in columns and then add as required. Let us consider some

    Read More

  5. Addition of Like Fractions | Examples | Videos | Worksheet | Fractions

    Apr 23, 25 09:23 AM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More