Answer:
T₄₀ = 241
Explanation:
the nth term of an arithmetic sequence is
= a₁ + d(n - 1)
a₁ is the first term and d the common difference
given a₅ = 31 and a₉ = 55, then using the nth term formula
a₁ + 4d = 31 → (1)
a₁ + 8d = 55 → (2)
subtract (1) from (2) term by term on both sides to eliminate a₁
(a₁ - a₁ ) + (8d - 4d) = 55 - 31
0 + 4d = 24
4d = 24 ( divide both sides by 4 )
d = 6
substitute d = 6 into either of the 2 equations and solve for a₁
substituting into (1)
a₁ + 4(6) = 31
a₁ + 24 = 31 ( subtract 24 from both sides )
a₁ = 7
Then nth term formula is
= 7 + 6(n - 1) = 7 + 6n - 6 = 6n + 1
now use this formula to find T₄₀
T₄₀ = 6(40) + 1 = 240 + 1 = 241