Week 1- My Arithmetic Sequence

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In the first week of Precalc, we have been taught about Arithmetic Sequences/Series and how to find t_n , S_n , d (common difference), and so much more. Example:

My sequence is:

7,4,1,-2,-5

Find the general equation for t_n :

t_n = t_1 + (n-1)d

t_n = 7+(n-1)(-3)

t_n = 7+(-3n)+3

t_n = -3n+4

t_n stands for the last known term for the sequence.

Find t_{50} :

t_n = t_1 + (n-1)d

t_{50} = t_1 + (50-1)(-3)

t_{50} = 7 + 49(-3)

t_{50} = 7 + (-147)

t_{50} = -140

Find S_n :

S_n = \frac{n}{2} (t_1 + t_n)

S_{50} = \frac{50}{2} (7 + -140)

S_{50} = 16.7 (-130)

S_{50} = -2171

 

 

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