How many terms of Arithmetic Progression 45,39,33,...must be taken so that their sum is 180? Explain the double answer
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Answered by
6
10 and 6 because it make a quadratic equation....
Answered by
5
Answer:
Step-by-step explanation:
Let Sₙ be the sum of the first n terms of an arithmetic progression.
The formula for getting the sum is therefore given by:
sₙ = n/2[2a + (n - 1)d]
In this formula :
n = Number of terms
a = the first term
d = the common difference.
The common difference is :
d = -6
a = 45
Doing the substitution we have :
180 = n/2[90 + (n - 1)-6]
180 × 2 = n(90 - 6n + 6)
360 = 96n - 6n²
We form a quadratic equation as follows:
6n² - 96n + 360 = 0
Divide through by 6 we have :
n² - 16 + 60 = 0
The roots are:
-10 and - 6
n² - 10n - 6n + 60 = 0
n(n - 10) -6(n - 10) = 0
(n - 6)(n - 10) = 0
n = 10 or 6
if we take n = 10
= 10/2(90 + (10 - 1)-6)
= 5(36) = 180
If we take n = 6 :
= 6/2(90 + (6 - 1)-6)
= 180
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