A sequence is defined by for .

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

A sequence is defined by

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

for

k \in \mathbb{N}

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

n

th term in the form

a + (n-1)d

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

n

for which the

n

th term is negative.