Mathematics

Problem

For a certain arithmetic progression the sum of the first

n

terms is given by

S_n = 3n^{2} + 5n

for every natural number

n

. a. (i) Express the

n

th term

T_n

of the progression in terms of the sums

S_n

and

S_{n-1}

. b. (ii) Using the relation found in part (i), write down the first three terms of the progression. c. (iii) Hence find the first term and the common difference of the progression.

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