Question

how many terms of the series 24+20+16....must be taken to give sum of 72? give reason for your answer​

Answer 1

Answer:

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Answer 2

$\fontsize{18}{10}{\textup{\textbf{Sum of first 4 or 9 terms is 72.}}}$

Step-by-step explanation:

The given series is

24 + 20 + 16 + .  .  .  .

We see that

$20-24=16-20=~~.~~.~~.~~=-4.$

So, the given series is an Arithmetic series with first term a and common difference d as follows :

a = 24  and d = -4.

We know that the sum of first n terms of an arithmetic series ith first term a and common difference d is

$S_n=\dfrac{n}{2}(2a+(n-1)d).$

Therefore, we must have

$\dfrac{n}{2}(2\times24+(n-1)(-4))=72\\\\\Rightarrow n(24-2n+2)=72\\\\\Rightarrow n(-2n+26)=72\\\\\Rightarrow n(-n+13)=36\\\\\Rightarrow n^2-13n+36=0\\\\\Rightarrow n^2-9n-4n+36=0\\\\\Rightarrow (n-4)(n-9)=0\\\\\Rightarrow n=4,9.$

Thus, the sum of first 4 terms or first 9 terms is 72.

#Learn more

Question : How many terms of the series 2+5+8+.... ....+610?​

Link : https://brainly.in/question/12968646.