I need some help here! We've been given the formula for Arithmetic and Geometric Progressions but the problems below, I cannot apply the formula. Its kinda tricky. Would you help me? These are sample questions for our long test. I need these so I can reviewT_T
1 Find an arithmetic progression if the sum of its first four terms is equal to 26 and the product of the same terms equals 880.
2. An arithmetic progression consists 20 terms. The sum of the terms occupying even places equals 259 while that of the terms occupying odd places equals 220. Find the two medium terms of the progression.
3 Find the four numbers forming a geometric progression in which the sum of the extremes is 27 and the product of the means is 72.
THANK YOU VERY MUCH.
Remember, an arithmetic progression is
where d is the common difference. So if we sum up all of the first FOUR terms say, that's
, now divide both sides by 2 and you get
So we make the reasonable guess that
, which by
. Now we check, does this indeed work? Well, we get:
, so we're good.
(If this had not worked, we'd next try
which would give
, but that one doesn't work. Basically try the nice numbers until you get one that works.
2. This time I'll start the first term calling it
and you'll see why, then the even terms are:
which is impossible because the left side is even and the right side is not. Even if you assume the first term is the zeroth term, you'll end up with an even thing on the left because it will be
3. Again, four numbers, label the common ratio as r, and then we get:
The sum of the extremes is
, but I don't understand what you mean by "means" which mean are you talking about? Which numbers are you averaging to get these means?