Question

Question in the photo :) (Please help with my other questions!)

Answer 1

a

Explanation:

the nth term of an arithmetic sequence is

`u_(n)` = u₁ + (n - 1)d

given u₂₀ = 100 and u₂₅ = 115 , then

u₁ + 19d = 100 → (1)

u₁ + 24d = 115 → (2)

subtract (1) from (2) term by term to eliminate u₁

0 + 5d = 15

5d = 15 ( divide both sides by 5 )

d = 3

substitute d = 3 into (1) and solve for u₁

u₁ + 19(3) = 100

u₁ + 57 = 100 ( subtract 57 from both sides )

u₁ = 43

Answer 2

a) u₁ = 43, d = 3

Explanation:

Given :-

u₂₀ = 100

u₂₅ = 115

To Find :-

u₁ and d

Solving :-

u₂₀ = u₁ + 19d = 100 -(1)

u₂₅ = u₁ + 24d = 115 -(2)

(2) - (1)

5d = 15

d = 3

u₁ + 19(3) = 100

u₁ + 57 = 100

u₁ = 43

Solution :-

a) u₁ = 43, d = 3