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Question

If the sum of the series 24,20,16,.... is 60. Find the number of terms in the series.


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Solution

Step 1. Find the number of terms in the series.

As we know that, an arithmetic progression is a sequence of numbers such that the difference d between each consecutive term is a constant.

The series are, a,a+d,a+2d,a+3d,....

The nth term is,

Tn=a+(n-1)×d

Here, Tn is the nth term, a is first term, n is the number of terms in the sequence and d is the common difference.

Sum of the first nth terms is given as,

Sn=n2[2a+n-1×d]

Where, Sn is the sum of a term of A. P. , a is first form of A. P. , d is common difference and n is the number of terms.

Step 2. Using the formula of sum of the first nth term.

We will find the number of terms by using the formula sum of the first nth terms.

Sn=n22a+n-1×d

Here,

Sn=60

a=24

d=20-24

=-4

So,

60=n2224+n-1×-4

120=n48-4n+4

4n2-52n+120=0

Divide each side by 4.

n2-13n+30=0

n-10n-3=0

So,

n-10=0

n=10

And

n-3=0

n=3

Hence, the number of terms in the series is 10 or 3.


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