MAT 112 Quiz #9 Name: ________________________

Some useful formulas

The sum of a finite arithmetic sequence	Sn = n/2 (a1 + an)
The n^th term of an arithmetic sequence	an = dn + c, where c = a1 - d
An alternative recursive formula	an = a1 + (n - 1)d
Recursive formula, arithmetic sequence	an+1 = an + d

(5pts)

Write an expression for the most apparent n^th term of the sequence. (Assume n begins with 1.)

	2/1,	3/3,	4/5,	5/7,	6/9,
index: n =	1,	2,	3,	4,	5,

Each value of the numerator is one higher than its index, n + 1.

Each value of the denominator is one less than twice its index, 2n -1.

So the formula is a_n = (n + 1)/(2n -1).

(5pts)

Find the n^th partial sum of the arithmetic sequence.

2, 8, 14, 20, ... n = 30

The common difference, d, is 6. The shift, c = a₁ - d = 2 - 6 = -4.
So a_n = 6n - 4. a₃₀ = 6(30) -4 = 176.

S₃₀ = 30/2 (2 + 176) = 2670.

Essential Trigonometry, Math Links

by Jack Tompkins