Find the 12th term from the end of the following arithmetic progressio

1.	Find the 12th term from the end of the following arithmetic progression : 1, 4, 7, 10, … 88
Answer» A.P is known for Arithmetic Progression whose common difference = a_n – a_n-1 Where n > 0 a = a₁ = 1, a₂ = 4, l = 88 Common difference, d = a₂ – a₁ = 4 – 1 = 3 We know, n^th term from end, b_n = l – (n – 1)d Where l is last term or a₁ and d is common difference and n is any natural number ∴ b₁₂= 88 – (12 – 1)3 ⇒ b₁₂ = 88 – 36 + 3 ⇒ b₁₂ = 91 – 36 ⇒ b₁₂ = 55 Hence, 12^th term from end for the given A.P is 55.

Find the 12th term from the end of the following arithmetic progression : 1, 4, 7, 10, … 88

Answer»

A.P is known for Arithmetic Progression whose common difference = a_n – a_n-1

Where n > 0

a = a₁ = 1, a₂ = 4, l = 88

Common difference,

d = a₂ – a₁

= 4 – 1

= 3

We know,

n^th term from end,

b_n = l – (n – 1)d

Where l is last term or a₁ and d is common difference and n is any natural number

∴ b₁₂= 88 – (12 – 1)3

⇒ b₁₂ = 88 – 36 + 3

⇒ b₁₂ = 91 – 36

⇒ b₁₂ = 55

Hence,

12^th term from end for the given A.P is 55.