Mathematics, 17.03.2020 20:32, loveoneonly9154

Please help which sigma notation is equivalent to the following series (check picture)

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answered: michaellagann2020

Step-by-step explanation:

Okay so what we are going to do here is look at our terms first and see what gets us there.

So lets consider the first term or the first sum, when k=1.

So if k=1 then the expression should give us a positive 5. So lets check each one for a +5.

So lets start with (5k-5) if we let k equal one this first term would be 0. So this doesnt work already.

The rest however do work so we need to keep checking.

Lets let k=2

We know that when k=2 we need the value of the term to equal -5.

So lets look at (-5k+10) if we let k be -5 then this second term would be 0 and 0 is not equal to -5 so this is now out.

Now lets look at (15k-10) if we let k=2 then this is (30-10) = 20 and 20 doesnt equal 5 so that not gonna work.

So our answer here must be (-10k+15). If we let k=2 then thats (-20+15) = -5

Now just to be 100% sure lets check some other terms. Lets check the last term which would be -755. This term would be the the 77th term so lets let k=77.

(-10(77) + 15) = -770 + 15 = -755. So that also works.

Hence our answer is the series/answer choice c.

answered: Guest

(6,0) i hope it makes enough sense

answered: Guest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.