4. Given the sequence: { -15, -11,- 7, - 3, ... 173 }

Question

a. Is this an arithmetic sequence?

b. Find the formula of the general term.

c. Determine the number of terms in the sequence.

Answer 1

a) The sequence is an arithmetic sequence if and only if the following condition is true,

a_n - a_n+1 = a_n+1 - a_n ∀n >0

So, -11 - (-15) = 4 = -7 - (-11)

Hence the given sequence is an arithmetic sequence.

b) Tn = a + (n-1)d

So, the formula for the given sequence is, Tn = -15 + (n-1)*4 = 4n - 19

c) Tn = 4n - 19 where, Tn = 173

so, 173 = 4n - 19

or 192/4 = n

or n = 48

So there are a total of 48 terms