TMUA 2022 Paper 2 Q8 — Worked Solution

P2·Sequences & Series, Logic & Quantifiers·6.5Official · 2022 · Q8

pigeonholearithmetic-sequencepairing

A selection,

S

, of

n

terms is taken from the arithmetic sequence

1, 4, 7, 10, \dots, 70

.Consider the following statement:

(∗)

There are two distinct terms in

S

whose sum is

74

What is the smallest value of

n

for which

(*)

is necessarily true?

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