Mathematics

Problem

A sequence is defined by

a_k = 7 - \dfrac{k}{2}

for

k \in \mathbb{N}

. a. (i) Show that the sequence forms an arithmetic progression. b. (ii) Express the

n

th term in the form

a + (n-1)d

and hence state the common difference. c. (iii) Find the smallest positive integer

n

for which the

n

th term is negative.