Math, asked by anshujain1003, 1 year ago

How many terms of Arithmetic Progression 45,39,33,...must be taken so that their sum is 180? Explain the double answer

Answers

Answered by ghostrider125
6

10 and 6 because it make a quadratic equation....

Answered by santy2
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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