(ii) If the 50th and 51st terms of an arithmetic sequence are
140 and 142, find the 1st term.

a₁ = 42

Step-by-step explanation:

The nth term of an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₅₀ = 140 and a₅₁ = 142 , then

a₁ + 49d = 140 → (1)

a₁ + 50d = 142 → (2)

Subtract (1) from (2) term by term to eliminate a₁

0 + d = 2

d = 2

Substitute d = 2 into (1)

a₁ + 49(2) = 140

a₁ + 98 = 140 ( subtract 98 from both sides )

a₁ = 42