The -th term of a sequence is defined by .

MATHEMATICS · Multi-part · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

The

n

-th term of a sequence is defined by

a_n = 3n + 7

. (i) Show that the sequence is an arithmetic progression and determine its first term and common difference. (ii) Find the smallest value of

n

for which

a_n

exceeds 100. (iii) Within the first 100 terms of the progression, determine how many terms are divisible by 5. Show your reasoning.