- #1

forevergone

- 49

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I was wondering about this when it hit me, can a sequence ever be both arithmetic and geometric?

I was thinking maybe a sequence like 0, 0, 0, 0... or 1, 1, 1, 1... where it's constant but I don't know thoroughly if there are any restrictions on arithmetic and geometric sequences that prohibit situations like these.

Could this be possible?

My second question is: An arithmetic sequence with general term A(n), n>=1 has the sum of the first two terms 5 and the sum of third and fourth terms 17. Find [tex]\sum_{i=1}^{10}{Ai} [/tex]

I don't really have an idea of how to approach this.

We know that:

[tex]A1 + A2 = 5[/tex]

[tex]A3 + A4 = 17[/tex]

But in the arithmetic sequence, how would you find [tex]a[/tex] or [tex]d[/tex]?

I was thinking maybe a sequence like 0, 0, 0, 0... or 1, 1, 1, 1... where it's constant but I don't know thoroughly if there are any restrictions on arithmetic and geometric sequences that prohibit situations like these.

Could this be possible?

My second question is: An arithmetic sequence with general term A(n), n>=1 has the sum of the first two terms 5 and the sum of third and fourth terms 17. Find [tex]\sum_{i=1}^{10}{Ai} [/tex]

I don't really have an idea of how to approach this.

We know that:

[tex]A1 + A2 = 5[/tex]

[tex]A3 + A4 = 17[/tex]

But in the arithmetic sequence, how would you find [tex]a[/tex] or [tex]d[/tex]?

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