For an A.P., the sum of its term is 60, common difference is 2 and last term is 18. find the number of term in A.P.
Answers
The number of terms = 4 for a = 12 , number of terms = 15 , for a = -10.
Given the sum of an A.P is 60 , d(common difference)= 2, last term = 18.
a = first term of the A.P
n = total number of terms in the A.P
Sum = n/2 ( first term + last term)
=> 60 = n/2 (a+18)
=> 120/(a+18) = n
Last term of the A.P = 18
=> 18 = a + (n-1)2
=> 18 = a + 240/(a+18) -2 {120/(a+18) = n}
=> 20(a+18) = a² + 18a + 240
=> 20a + 360 = a² + 18a + 240
=> a² - 2a -120 = 0
=> a²- 12a + 10a -120 = 0
=> a = 12 , -10
For a = 12 , n = 4
For a = -10 , n = 15
Two values of n are possible for different values of the first term of the A.P.
The number of terms = 4 for a = 12 , number of terms = 15 , for a = -10.
Given the sum of an A.P is 60 , d(common difference)= 2, last term = 18.
a = first term of the A.P
n = total number of terms in the A.P
Sum = n/2 ( first term + last term)
=> 60 = n/2 (a+18)
=> 120/(a+18) = n
Last term of the A.P = 18
=> 18 = a + (n-1)2
=> 18 = a + 240/(a+18) -2 {120/(a+18) = n}
=> 20(a+18) = a² + 18a + 240
=> 20a + 360 = a² + 18a + 240
=> a² - 2a -120 = 0
=> a²- 12a + 10a -120 = 0
=> a = 12 , -10
For a = 12 , n = 4
For a = -10 , n = 15