Arithmetic Sequence

Arithmetic Progression

This is the formula to find the certain term of an arithmetic progression

a_n = a_1 + (n - 1)d,

"a" is a progression
"n" indicates the term
"d" indicates the difference between each term.

Some Questions

1)
4k - 2, 18, 9k - 1 are the consecutive term of an arithmetic sequence, hence find k

2)
Find the general term of an arithmetic sequence when the eighth term is -8 and the fourteenth term is -11

Solutions

1)
The hint of the question one is that they are consecutive. Meaning that the difference should be the same so:

18 - (4k - 2) = 9k - 1 -18

20 - 4k = 9k - 19

39 = 13k

k = 3

2)
First use the formula of the arithmetic progression and make the first therm the subject

${a_n} - (n - 1)d = {a_1}$

Since the first term should be the same for both terms we can form an equation

-8 - (8-1)d = -11 - (14-1)d

-8 - 7d = -11 -13d

6d = -3

d = -1/2

if d = -1/2 we can deduce the first term

-8 - 7d = -8 +3.5 = -4.5

so the general formula is this

${u_n} = - 4.5 + (n - 1)( - 1/2)$