Question

The first three terms of an arithmetic sequence are u1=0.5

Answer 1

Answer:

1)Common difference=1.3 as 3.1-1.8=1.3 also 1.8-0.5=1.3

2)Method to take out Progression

a+(n-1)d=tn

0.5+(30-1)1.3=tn

0.5+37.7=38.2

3)580.5

Answer 2

Answer:

see explanation

Step-by-step explanation:

(a)

The common difference d = u₂ - u₁ = 1.8 - 0.5 = 1.3

(b)

The nth term of an arithmetic sequence is

$u_{n}$ = u₁ + (n - 1)d

Here u₁ = 0.5 and d = 1.3 , then

u₃₀ = 0.5 + (29 × 1.3) = 0.5 + 37.7 = 38.2

(c)

The sum to n terms of an arithmetic sequence is

$S_{n}$ = $\frac{n}{2}$ [ 2u₁ + (n - 1)d ] , then

$S_{30}$ = $\frac{30}{2}$ [ (2 × 0.5) + (29 × 1.3) ]

     = 15(1 + 37.7)

    = 15 × 38.7

    = 580.5