Respuesta :
20 terms on the right side of the given equation [tex]20=20+18+16+...+x[/tex].
How we find the sum of n terms?
The first n terms of the arithmetic sequence are added together to form the sum of the first n terms of AP.
Therefore, we can only evaluate the sum of n terms in a sequence if we are aware of the type of sequence it is. Usually, when calculating the sum of an n-number of terms, we take into account arithmetic progression. The common distinction between each following term and each preceding term remains unchanged throughout this progression. Natural numbers are an illustration of Arithmetic Progression, where the common difference is 1. We must therefore be familiar with the formula in order to calculate the sum of natural numbers.
We can use formula for sum of n terms-
[tex]S = \frac{n}{2}(2a + (n-1)d)[/tex]
where, S- sum of n terms
n- number of terms
a- first term
d- difference between two consecutive terms
Here, S= 20 , a = 20, d= -2
we have to find n,
[tex]S = 20 = \frac{n}{2}(2(20) + (n-1)(-2)) \\20 = \frac{n}{2}(40-(2n-2))\\40 = n(40-2n+2)\\40 = 42n-2n^2\\2n^2 -42n +40 = 0[/tex]
solving this quadratic equation-
[tex]2n^2 -42n +40 = 0\\2n^2 -40n-2n+40=0\\2n(n-20)-2(n-20) = 0\\(2n-2)(n-20)=0[/tex]
when,
[tex]2n-2 = 0\\n=1[/tex]
When,
[tex]n-20=0\\ n=20[/tex]
as we can see that there are more than 1 terms present in the series so answer will be 20 terms.
To learn more about Arithmetic Progression from the below link
https://brainly.com/question/6561461
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