Answer 1

A.P. = 16, 11, 6, 1, ...

It is given that

t_n = – 54

a = 16, d = t₂ – t₁ = 11 – 16 = – 5

∴ t_n = a + (n – 1)d

– 54 = 16 + (n – 1)(– 5)

– 54 = 16 – 5n + 5

21 – 5n = – 54

– 5n = – 54 – 21

– 5n = – 75

n = `75/5` = 15

∴ 15^th term is – 54.