227k views
17 votes
The 8th term of a linear sequence is 18 and the 12th term is 26. Find the first term, the common difference and the 20th term

1 Answer

3 votes

Answer:

see explanation

Explanation:

the sequence is linear, that is arithmetic with nth term


a_(n) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₈ = 18 and a₁₂ = 26 , then

a₁ + 7d = 18 → (1)

a₁ + 11d = 26 → (2)

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

4d = 8 ( divide both sides by 4 )

d = 2

substitute d = 2 into (1) and solve for a₁

a₁ + 7(2) = 18

a₁ + 14 = 18 ( subtract 14 from both sides )

a₁ = 4

then

a₂₀ = 4 + (19 × 2) = 4 + 38 = 42

User Chrysillo
by
6.3k points