Question

Q. 4. Which term of the A.P. 3, 8, 13, 18,..... is 78?​

Answer 1

Answer:

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Answer 2

Answer :

n = 16

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 .

Solution :

• Given AP : 3 , 8 , 13 , 18 , . . .
• To find : If a(n) = 78 , then n = ?

Here ,

The given AP is 3 , 8 , 13 , 18 , . . . , 78

Clearly ,

First term , a = 3

Common difference , d = 8 - 3 = 5

nth term , a(n) = 78

Also ,

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

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

=> 78 = 3 + (n - 1)•5

=> 5•(n - 1) = 78 - 3

=> 5•(n - 1) = 75

=> n - 1 = 75/5

=> n - 1 = 15

=> n = 15 + 1

=> n = 16

Hence ,

78 is the 16th term of the given AP .