Dom's blog

Chapter 13-1

formulas:
Arithmetic = tn = t1+(n-1)d
Geometric = tn = t1 x r^n-1

Example 1:

3, 7, 11, 15, 19 has a₁ = 3, d = 4,

and n = 5. The explicit formula is

a_n = 3 + (n – 1)·4 = 4n – 1

Example 2:

These two terms are 12 – 5 = 7 places apart, so, from the definition of a geometric sequence, I know that a₁₂ = ( a₅ )( r⁷ ). I can use this to solve for the value of the common ratio r:

160 = (5/4)(r⁷)
128 = r⁷
2 = r

Since a₅ = ar⁴, then I can solve for the value of the first term a:

5/4 = a(2⁴) = 16a
5/64 = a

well thats it