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Q1)What is the sum of the finite arithmetic series −10, −8, −6, −4, ...24?
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Q2)You are trying to save $1500. You begin with $5 and save $3 more than the previous amount each week for 30 weeks. Will you meet your goal? Explain. Show work

Sagot :

Solution :

First term, a₀ = -10 .

Common difference of A.P. , d = -8 - (-10) = 2 .

Last term, aₙ = 24 .

We know, last term is given by :

aₙ = a₀ + (n-1)d

24 = -10 + (n-1)×2

2n - 2 = 34

n = 18

Now, sum of series is given by :

[tex]S_n = \dfrac{n}{2} \times ( 2a+(n-1)d)\\\\S_n = \dfrac{18}{2} \times ( 2\times -10 + ( 18 -1) \times 2)\\\\S_n = 126[/tex]

Hence, this is the required solution.

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