# SOLVING WORD PROBLEMS INVOLVING ARITHMETIC SEQUENCE

Solving Word Problems Involving Arithmetic Sequence :

Here we are going to how we solve word problems involving the concept arithmetic progression.

## Solving Word Problems Involving Arithmetic Sequence - Examples

Question 1 :

The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

Solution :

a17  =   a10 + 7

a + 16d  =  a + 9d  + 7

a - a + 16d - 9d  =  7

7d  =  7

d  =  7/7  =  1

Hence the common difference is 1.

Question 2 :

Which term of the AP :

3, 15, 27, 39,.......... will be 132 more than its 54th term?

Solution :

an = 132 + a54

a + (n - 1) d = 132 + a + 53d

a = 3    d = 15 - 3  =  12

3 + (n - 1) 12  =  132 + 3 + 53 (12)

3 + 12 n - 12  =  135 + 636

-9 + 12 n  =  771

12 n  =  771 + 9

12 n  =  780

n  =  780/12  ==>  65

Question 2 :

Two APs have the same common difference. The difference between their 100th term is 100, What is the difference between their 1000th terms?

Solution :

Let the first two terms of two APs a₁ and a respectively and the common difference of these two A.Ps be d

for first A.P

a₁₀₀ = a₁ + (100 - 1) d

=  a₁ + 99 d

a₁₀₀₀ = a₁ + (1000 - 1) d

=  a₁ + 999 d

For second AP

a₁₀₀  =  a₂ + (100 - 1) d

=  a₂ + 99 d

a₁₀₀₀  =  a₂ + (1000 - 1) d

=  a₂ + 999 d

given that,

difference between two  100th term of two APs = 100

(a₁ + 99 d) - (a₂ + 99 d) = 100

a₁ + 99 d - a₂ - 99 d = 100

a₁ - a₂ = 100

difference between 1000th term of two APs

= (a₁ + 999 d) - (a₂ + 999 d)

= a₁ + 999 d - a₂ - 999 d

= a₁ - a

= 100

Difference between 1000th term of two APs = 100

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

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