Question

2. Find the common difference and 15th term of the A.P. 125, 120, 115, 110, g.

Answer 1

AP ( Arithmetic progression).
An arithmetic progression is a list of numbers a1, a2, a3 ………….. an in which each term is obtained by adding a fixed number to the preceding term except the first term.
This fixed number is called the common difference( d ) of the AP. Common difference of an AP will be the difference between any two consecutive terms.

a2= a1+d
a3= a2+d
a4= a3+d
……..
an= an-1+d ………

Each of the numbers in the list is called a term .

Method to find the common difference :
d = a2 - a1 or a3 - a2 or a4 - a3...

General form of an AP.:
a, a+d, a+2d, a+3d…….

Here a is the first term and d is common difference.

General term or nth term of A.P
The general term or nth term of A.P is given by an = a + (n – 1)d, where a is the first term, d is the common difference and n is the number of term.

SOLUTION :
GIVEN :
A.P - 125,120,115,110…
Here a1 = 125 , a2 = 120, a3 = 115, a4= 110

Common Difference (d) = a2 - a1 = 120 - 125 = -5
d = -5

a =125 , d = -5 , n = 15
an = a + (n – 1)d
a15 = 125 +(15 - 1) ×-5
a15 = 125 +(14×-5)
a15 = 125 - 70
a15 = 55

Hence, the common difference (d) is -5 and 15th term is 55.

HOPE THIS WILL HELP YOU….

Answer 2

125 , 120 , 115 , 110 , .... is an A.P

First term = a = a1 = 125 ,

Common difference = d

d = a2 - a1

d = 120 - 125 = -5

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If a , d are first term and common

difference of an A.P then

nth term = an = a + ( n - 1 )d

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Here ,

a = 125 , d = -5 , n = 15

15 the term = a15

= a + ( 15 - 1 )d

= 125 + 14 × ( -5 )

= 125 - 70

= 55

Therefore ,

a15 = 55

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