Mathematics

Problem

Let

S_n

denote the sum of the first

n

terms of an arithmetic progression with first term

a

and common difference

d

. a. (i) Obtain an expression for

S_n - S_{n-1}

and interpret your result. b. (ii) Using your result from part (i), explain how the common difference

d

can be determined when the sums

S_m

and

S_n

of two different numbers of terms are known.