# How can I find the nth term if the partial sum is 490, the first term is -5 and n = 100?

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• The answer depends on the specific sequence. You didn't say if this was an arithmetic sequence (common difference), geometric sequence (common ratio) or some other type of sequence.

If we assume an arithmetic sequence, then the formula for the nth term is:

a[n] = a + d(n - 1)

And the partial sum of n terms is:

S[n] = n/2 * (a + a[n])

We know that:a = -5

n = 100

S = 490

Let's plug in the information into the partial sum formula:

S = 100/2 * (-5 + a[n]) = 490

a - 5 = 490 / 50

a - 5 = 49/5 = 9.8

a = 5 + 9.8

a = 14.8

If they then want you to find the formula for an arbitrary term, you would use the first formula:

a[n] = a + d(n - 1)

a = -5 + d(99) = 14.8

99d = 19.8

d = 19.8 / 99

d = 0.2

Final formula for any 'nth' term:

a[n] = -5 + 0.2(n - 1)

a[n] = -5 + 0.2(n - 1)

When n = 100:

a = -5 + 0.2(99) = -5 + 19.8 = 14.8

So the final formula

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• S = (n/2)(a + l) = (100/2)(-5+l)=490 --->l = 14.8

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