Question

How many terms of the A.P 24,21,18.... must be taken so that their sum is 78

Answer 1

Answer:

Step-by-step explanation:

first term, a = 24

common difference, d = 21-24 = -3

let the number of terms to get sum 78 is n.

 

Solving the quadratic equation, we get n=4 and n=13.

So you can take either 4 terms or 13 terms to get the sum 78.

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Answer 2

a=24,d=21-24=-3,sn=78.n=?

we use= sn=n/2(2a+(n-1)d)

78=n/2(48+(n-1)-3

78 = n/2(48-3n+3)

78=n/2(51-3n)

78*2=51n-3n2

156=51n-3n2

3n2-51n+156=0

3(n2-17n+52)=0

n2-17n+52=0

n2-4n-13n+52=0

n(n-4)-13(n-4)=0

(n-13),(n-4)=0

(n-13)=0,(n-4)=0

n=13,n=4

so.both the values of n.so.the number of terms is either 13 or 4.
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