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