## HOW TO FIND THE TOTAL NUMBER OF TERMS IN AN ARITHMETIC SEQUENCE

How to find the total number of terms in an arithmetic sequence?

By using the formula

n = [(L- a)/d] + 1

we can find the total number of terms of an arithmetic sequence.

L - Last term

a  =  first term

d  =  common difference (a2 - a1)

## Example Problems of Finding Total Number of Terms of Arithmetic Progression

Question 1 :

How many terms are there in the following Arithmetic progressions ?

-1,-5/6,-2/3,……………10/3

Solution :

First term (a)  =  -1

Common difference (d)  =  a2 – a1

d  =  (-5/6) – (-1)

d  =  1/6

n  =  [(L-a)/d] + 1

L  =  10/3 n  =  27

Hence, 27 terms are in the given A.P

Question 2 :

How many terms are there in the following Arithmetic progressions ?

7, 13, 19,……………205

Solution :

First term (a) = 7

Common difference  (d) = a2 – a1

d  =  13 – 7

d  = 6

L  =  205

n  =  [(L - a)/d] + 1

n  =  [(205 - 7)/6] + 1

n  =  (198/6) + 1

n  = 34

Hence, 34 terms are in the given A.P

Question 3 :

The 10th and 18th terms of an A.P are 41 and 73 respectively. Find the 27th term

Solution :

10th term  =  41

a + 9 d  =  41   ------- (1)

18th term  =  73

a + 17 d  =  73   ------- (2)

Subtracting (2) from (1)

a + 17 d - (a + 9 d)  =  73 - 41

a + 17d - a - 9d  =  32

8d  =  32

d  =  4

By substituting the value of d in (1)

a + 9 (4)  =  41

a + 36 = 41

a = 5

Now, we have to find 27th term

an =  a + (n - 1) d

here n = 27

a27  =  5 + (27-1) 4

a27  =  5 + 26 (4)

a27  =  5 + 104

a27  =  109

Hence, 27th term of the sequence is 109.

Question 4 :

Find n so that the nth terms of the following two A.P’s are the same

1, 7, 13, 19, ………………. and 100, 95, 90 ,………..

Solution :

an =  a + (n - 1) d

nth term of the first sequence

a  =  1   d  =  t₂-t₁

d  =  7-1

d  =  6

an  =  1 + (n-1) 6

an  =  1 + 6n – 6

an  =  6n – 5   -----(1)

nth term of the second sequence

a  =  100   d  =  t₂ - t₁

d  =  95 - 100

d  =  -5

an  =  100 + (n-1)(-5)

an  =  100 - 5n + 5

an  =  105 - 5n -----(2)

nth terms of the above sequence are equal.

(1) = (2)

6n – 5  =  105 – 5n

6n + 5n  =  105 + 5

11n  =  110

n  =  110/11

n  =  11

Hence 11th terms of the given sequence are equal.

Question 5 :

How many two digit numbers are divisible by 13?

Solution :

Two digit numbers are

10, 11, 12,………… 99

Now we need to find how many terms from this sequence are divisible by 13

By writing the numbers divisible by 13 as sequence, we get

13, 26, 39, …………….. 91

Now, we need to find how many terms are there in this sequence for that let us use formula for n.

n  =  [(L-a)/d] + 1

a  =  13, d  =  26 – 13==> d  =  13,  L = 91

n  =  [(91 - 13)/13] + 1

n  =   (78/13) + 1

n  =  7

7 two digit numbers are divisible by 13. Apart from the stuff, if you need any other stuff in math, please use our google custom search here.

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

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 