SOLUTION: How many terms of an AP 17, 15, 13, 11�. must be added to get the sum 72? Explain the double answer.

Question 1063411: How many terms of an AP 17, 15, 13, 11�. must be added to get the sum 72?
Explain the double answer.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The common difference of this arithmetic progression is -2, then
:
72 = (n/2) * (2a + (n-1)d), where a is the first term, n is the number of terms and d is the common difference
:
72 = (n/2) * ( (2*17) + (n-1)*(-2) )
:
72 = (n/2) * ( 34 -2n + 2)
:
144 = n * ( 34 -2n + 2)
:
144 = 36n -2n^2
:
2n^2 -36n +144 = 0
:
n^2 -18n +72 = 0
:
(n - 12) * (n - 6) = 0
:
n = 12 or n = 6
:
************************************************************
The number of terms can be 12 or 6
:
Inspect the first 12 numbers in the sequence
:
17, 15, 13, 11, 9, 7, 5, 3, 1, -1, -3, -5
:
Note that 5, 3, 1 and -1, -3, -5 cancel each other in the sum
:
*************************************************************
:

RELATED QUESTIONS
How many terms of the series 5+9+13+17... Must be added so that the sum will be 230?... (answered by Edwin McCravy,ikleyn)

how many terms in the series 19+16+13...must be added to give a sum of... (answered by josgarithmetic)

How many terms in the series 19+16+13+... Must be added to a sum of... (answered by Edwin McCravy)

How many terms in the series 19+16+13 must be added to give a sum of... (answered by Edwin McCravy)

The sum to n terms of an arithmetic series is sn=n/2 +(7n+15).determine the 6th tern and... (answered by richwmiller)

Hello, how many terms of the sequence -19,-15,-11,... must be taken to give a sum of 98?... (answered by stanbon)

How many term of the series 19+17+15........... must be taken in order to get sum... (answered by Edwin McCravy)

how many terms of the series 24,20,16...must be taken that the sum may be... (answered by sachi)

If 1,1,3,9 be added respectively to four terms of an AP.,a GP results. Find the four... (answered by math_tutor2020,greenestamps)