Week 6: Sequences, Series, Binomial Theorem and Induction

Write the explicit formula for the geometric sequence.

3, -12, 48, -192, ...

• a_n = 4(3)^n-1

• a_n = 3(4)^n-1

• a_n = -4(3)^n-1

• a_n = 3(-4)^n-1

Find the common ratio (multiplier):  a₁ = 4 and a₄ = 256

• 84
• 64
• 4
• 8

Tags

CCSS.HSF.BF.A.2

What is the 14th term of the geometric sequence?

3, 9, 27, 81, ...

• 14,348,907

• 4,782,969

• 1,594,323

• 45

Find the partial sum  $S_6$  for the geometric series.

 $-\frac{4}{5}+8-80+...$ 

•  $S_6$   = 21,845

•  

   $S_6$  = 72,000

•  

   $S_6$ = 72,727.2

•  

   $S_6$  = -128,840.8

Which of the series below is CONVERGENT?

• $a_1=4$
  $a_n=a_{n-1}\cdot\left(1.5\right)$
  

• $a_n=-n^2-8n+106$

• $a_n=\left(\frac{5}{10}\right)^n$

• $a_n=5n+6$

 $\sum_{n=4}^{\infty}2\left(0.5\right)^{n-1}$  

 $\sum_{k=1}^{\infty}\left(\frac{2}{5}\right)^k$  Find the sum

•  $\frac{2}{5}$  

•  $\frac{2}{3}$  

• 0

•  $\infty$  

What is row 5 of Pascal's Triangle?

• 1, 2, 1
• 1, 3, 3, 1
• 1, 4, 9, 4, 1
• 1, 5, 10, 10, 5, 1

Expand  $\left(2x+4y\right)^3$ 

•  $8x^3+48x^2y+96xy^2+64y^3$  

•  $40x^3+160x^2y+320xy^2+320y^3$  

•  $32x^3+48x^2y+96xy^2+64y^3$  

•  $8x^3+16x^2y+32xy^2+64y^3$  

 Calculate the coefficient of  $a^4b^6$  in the expansion of  $\left(a+b\right)^{10}$  .