Question

If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.

Answer 1

Since (n – 2), (4n – 1) and (5n + 2) are in A.P., we have

(4n – 1) – (n – 2) = (5n + 2) – (4n – 1)

`\implies` 4n – 1 – n + 2 = 5n + 2 – 4n + 1

`\implies` 3n + 1 = n + 3

`\implies` 2n = 2

`\implies` n = 1

∴ (n – 2), (4n – 1) and (5n + 2)

∴ (1 – 2), (4(1) – 1) and (5(1) + 2)

So, the given numbers are –1, 3, 7

`\implies` a = –1 and d = 3 – (–1) = 4

Hence, the next two terms are (7 + 4) and (7 + 2 × 4) 

i.e 11 and 15