(Based on a general arithmetic progression) An arithmetic progression (AP) has first…

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

Problem

(Based on a general arithmetic progression) An arithmetic progression (AP) has first term

a

and common difference

d

. Answer the following: (i) Prove that the sum

S_n

of its first

n

terms can be expressed entirely in terms of

a

d

and

n

. (ii) For the AP with

a = 7

and

d = -3

, determine the least positive integer

n

for which the sum of the first

n

terms is negative. (iii) Using the value of

n

obtained in part (ii), calculate that negative sum. (iv) Find the sum of the first

20

terms of the AP in part (ii).