Is this sequence arithmetic, geometric or neither? 3.5. -4, -7.5...

Mathematics

1 answer:

kvasek [131]3 years ago

8 0

Answer:

Neither

Step-by-step explanation:

If the sequence was geometric, each term would be multiplied by the same multiplier to get to the next one. We can check if the multiplier is the same by taking a term and dividing it by the term before it. For example,

-4/3.5=-1.14285714

-7.5/-4=1.87500

The multiplier between the terms aren't the same so it's not geometric.

For arithmetic, the distances between each term would be the same, and we can take the same idea from the geometric sequence, but use subtraction instead of division

-4-3,5=-7.5

-7.5-(-4)=-3.5

Again, the distances aren't the same, so it's not arithmetic.

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If you were to compute $\frac{1-\sqrt{1+160\pi^2}}{2\pi}$ you should get roughly -6.167402596 as your other solution. Each solution can then be plugged into the original equation to check if you get 0 or not. You likely won't land exactly on 0 but you'll get close enough.