In this section, we are going to see some example problems in arithmetic sequence.

General term or n^{th} term of an arithmetic sequence :

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

where 'a_{1}' is the first term and 'd' is the common difference.

Formula to find the common difference :

**d = a _{2} - a_{1}**

Formula to find number of terms in an arithmetic sequence :

**n = [(l - a _{1}) / d] + 1**

where 'l' is the last term, 'a_{1}' is the first term and 'd' is the common difference.

General form of an arithmetic sequence :

**a _{1}, (a_{1 }+ d), (a_{1 }+ 2d), (a_{1 }+ 3d),.........**

where 'a_{1}' is the first term and 'd' is the common difference.

**Problem 1 : **

The first term of an A.P is 6 and the common difference is 5. Find the arithmetic sequence its general term.

**Solution :**

a_{1} = 6

d = 5

**Arithmetic Sequence : **

a_{1}, (a_{1 }+ d), (a_{1 }+ 2d), (a_{1 }+ 3d),....................

Substitute 6 for a_{1} and 5 for d.

6, (6_{ }+ 5), (6_{ }+ 2 ⋅ 5), (6_{ }+ 3 ⋅ 5),....................

6, 11, 16, 21,....................

**General Term : **

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

Substitute 6 for a_{1} and 5 for d.

a_{n} = 6 + (n - 1)5

a_{n} = 6 + 5n - 5

a_{n} = 5n + 1

**Problem 2 : **

Find the common difference and 15^{th} term of an arithmetic sequence :

125, 120, 115, 110,...............

**Solution :**

a_{1} = 125

a_{2}_{ }= 120

**Common Difference :**

d = a_{2} - a_{1 }

d = 120 - 125

d = -5

**15 ^{th} Term :**

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

Substitute 15 for n, 125 for a_{1} and -5 for d.

a_{15} = 125 + (15 - 1)(-5)

a_{15} = 125 + (14)(-5)

a_{15} = 125 - 70

a_{15} = 55

**Problem 3 : **

Which term of the arithmetic sequence 24, 23¼, 22½, 21¾, ……… is 3?

**Solution :**

a_{1} = 24

d = a_{2} - a_{1 }= 23¼ - 24 = -3/4

Let 3 be the nth term of the given arithmetic sequence.

Then,

a_{n} = 3

a_{1} + (n - 1)d = 3

Substitute 24 for a_{1} and -3/4 for d.

24 + (n - 1)(-3/4) = 3

96/4 - 3n/4 + 3/4 = 3

(96 - 3n + 3) / 4 = 3

(-3n + 99) / 4 = 3

Multiply each side by 4.

-3n + 99 = 12

Subtract 99 from each side.

-3n = -87

Divide each side by -3.

n = 29

Therefore, 3 is 29^{th} term in the given arithmetic sequence.

**Problem 4 : **

How many terms are in the following arithmetic sequence ?

7, 11, 15,……………483

**Solution :**

a_{1} = 7

d = a_{2} - a_{1 }= 11 - 7 = 4

Formula to find number of terms in an arithmetic sequence :

n = [(l - a_{1}) / d] + 1

Substitute 483 for l, 7 for a_{1} and 4 for d.

n = [(483 - 7) / 4] + 1

n = [476 / 4] + 1

n = 119 + 1

n = 120

Therefore, there are 120 terms in the given arithmetic sequence.

**Problem 5 : **

The 10^{th} and 18^{th} terms of an arithmetic sequence are 41 and 73 respectively. Find the 27th term

**Solution :**

a a a |
a a a |

Solving (1) and (2),

a_{1} = 5

d = 4

**27th Term : **

**a _{27} = a_{1} + (27 - 1)d**

**a _{27} = a_{1} + 26d**

**Substitute 5 for a _{1} and 4 for d. **

**a _{27} = 5 + 26(4)**

**a _{27} = 5 + 104**

**a _{27} = 109**

After having gone through the stuff given above, we hope that the students would have understood how to solve problems in arithmetic sequence.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**