Question

15. If 5 + 7+9+ ...... + x = 320, then x is equal to ...

Answer 1

$\huge\bold{Answer:}$


5 + 7 + 9 + 11 + x = 320

→ 32 + x = 320

→ x = $\frac{320}{32}$

→ x = 10


X is equal to 10

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The required value of x is 35.}}}$

Step-by-step explanation:

We are given to find x such that

5 + 7 + 9 +  .  .  .  .  .  .  + x = 320.

The left hand side of the above equation is an arithmetic series with first term, a = 5  and common difference, d = 7 - 5 = 9 - 7 =  .  .  .  = 2.

Also, the sum of first n terms of an arithmetic series with first term a and common difference d is

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

Let the sum of first n terms be 320. So, we must have

$\dfrac{n}{2}(2\times5+(n-1)2)=320\\\\\Rightarrow n(5+n-1)=320\\\\\Rightarrow n^2+4n-320=0\\\\\Rightarrow n^2+20n-16n-320=0\\\\\Rightarrow (n-16)(n+20)=0\\\\\Rightarrow n=16,-20.$

Since the number of terms cannot be negative, so n = 16.  

Therefore, the sum of first 16 terms is 320 and the 16th term is given by

$a_{16}=a+(16-1)d=5+(16-1)\times2=5+30=35.$

Thus, the required value of x is 35.

#Learn more

Question : How many terms of the A. P. 3,5,7,9.....must be added to get the sum 120?

Link : https://brainly.in/question/5133504.