Which term of the Arithmetic Progression –7, –12, –17, –22

• Arithmetic Progression (C10)

Which term of the Arithmetic Progression –7, –12, –17, –22, ... will be –82 ? Is –100 any term of the A.P. ? Give reason for your answer.

Answer

Let –82 = a_n

∴ –82 = –7 + (n – 1)(–5)

⇒ 15 = n – 1

n = 16

Again

–100 = a_m = –7 + (m – 1)(–5)

⇒ (m – 1)(–5) = –93

m – 1 = 93/5

m = 93/5 + 1 ∉ N

∴ –100 is not a term of the AP.