Week 10- Midterm Review

In Week 10 of Pre-Valc we reviewed all of the 4 units to prepare ourselves for the midterm. While reviewing I am strong in understanding the graphing unit since we just convered that and I am confident in solving radical equations, but during my review I paid extra attention to the first unit were we covered arithmetic/geometric sequences and series.

Arithmetic Sequences:

  • It is the pattern of the Sequence (adding numbers or subtracting numbers)
  • The common difference (d) is the number that the pattern adds or subtracts by
  • You can find t_n by using the formula  = t_1 + (n-1)d

Arithmetic Series

  • It is the sum of the n terms of a sequance
  • You can find the S_n by using the formula S_n = \frac{n}{2} (t_1 + t_n) or S_n = \frac{n}{2} (2t_1 + (n-1)d) if you don’t know the t_n

Geometric Sequence

  • Each of the terms is multiplied by a number, know as the common ratio (r)
  • to find t_n use the formula t_n = a r^{n-1}

Geometric Series

  • It is the sum of the terms
  • In a Geometric Series their can be a diverging series with no sum; when a geometric series diverges that means that the numbers are getting bigger
  • Or a converging series with a infinite sum; When a geometric series converges that means that the numbers are getting closer together
  • To find the S_n use the fomula S_n = a ( r^n - 1) \div \ (r-1)
  • To find the S_\infty use the formula S_\infty = \frac {a}{1-r}

Leave a Reply

Your email address will not be published. Required fields are marked *