Question

for the AP 9,18,27,...., write the first term and common difference. also write the fifth term​

Answer 1

Answer :

1st term , a = 9

Common difference , d = 9

15th term , a(15) = 135

Note :

★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.

★ If a1 , a2 , a3 , . . . , an are in AP , then

a2 - a1 = a3 - a2 = a4 - a3 = . . .

★ The common difference of an AP is given by ; d = a(n) - a(n-1) .

★ The nth term of an AP is given by ;

a(n) = a + (n - 1)d .

★ If a , b , c are in AP , then 2b = a + c .

★ The sum of nth terms of an AP is given by ; S(n) = (n/2)×[ 2a + (n - 1)d ] .

or S(n) = (n/2)×(a + l) , l is the last term .

★ The nth term of an AP can be also given by ; a(n) = S(n) - S(n-1) .

Solution :

• Given AP : 9 , 18 , 27 ....
• To find : a , d , a(15) = ?

Clearly ,

First term , a = 9

Also ,

Common difference , d = 18 - 9 = 9

Now ,

We know that , the nth term of an AP is given by ;

a(n) = a + (n - 1)d .

Thus ,

The 15th term of the given AP will be given as ;

=> a(15) = a + (15 - 1)d

=> a(15) = a + 14d

=> a(15) = 9 + 14•9

=> a(15) = 9 + 126

=> a(15) = 135

Hence ,

1st term , a = 9

Common difference , d = 9

15th term , a(15) = 135

Answer 2

Step-by-step explanation:

135 is the answer of this