Question

How many terms does the AP -15,-12,-9………..15 have?​

Answer 1

Answer :

11

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 .

Solution :

• Given AP : -15 , -12 , -9 , . . . , 15
• To find : Number of terms , n = ?

Here ,

The given AP is -15 , -12 , -9 , . . . , 15 .

Clearly , we have ;

• First term , a = -15

• Common difference , d = -12 - (-15)

d = -12 + 15

d = 3

• Last term , a(n) = 15

Also ,

We know that ,

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

=> 15 = -15 + (n - 1)•3

=> 15 + 15 = 3(n - 1)

=> 30 = 3(n - 1)

=> n - 1 = 30/3

=> n - 1 = 10

=> n = 10 + 1

=> n = 11

Hence ,

The number of terms in the given AP is 11 .

Answer 2

Answer : 11

Explanation:

Here, 1st term (a¹) = -15

common difference(d) = a² - a¹

= -12 - (-15) = 3

let the number of terms in A.P be n

therefore,

15 = a¹ + (n-1)d

→15 = -15 + (n-1)3

→30 = (n-1)3

→10 = n-1

→n = 11

total number of terms in A.P = 11

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