Consider an arithmetic progression with first term and common difference .

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

Problem

Consider an arithmetic progression with first term

a

and common difference

d

. (i) Explain what is meant by the

n

-th term of the progression. (ii) Without writing the stated formula for

a_n

, construct the 6th term in terms of

a

and

d

. Generalise your reasoning to write an expression for the

n

-th term. (iii) Why does your expression contain the factor

(n-1)

instead of

n

? Give a brief explanation.