Write the series 1-0.5-2+ ... for 12 terms using summation notation

The summation notation for the given series is  

The given series is,

Since,    

Here we observe that,  common difference between each term is - 1.5.

So, given series is an Arithmetic progression series.

First term, , common difference,

General term for AP series,

Hence, summation series up to 12 terms is,

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The series

            1 -0.5-2-3.5 -5-6.5-8-9.5-11-12.5-14-15.5 upto 12 terms

Step-by-step explanation:

Step(i):-

Given series  1 -0.5 -2 +

we know that the sum of the sequence is called a series

The sequence is 1, -0.5, -2, -3.5,is in AP

a = 1 and the difference between the two terms is equal 'd' = -1.5

Step(ii):-

adding 1.5 value of each term

The series

            1 -0.5-2-3.5 -5-6.5-8-9.5-11-12.5-14-15.5 upto 12 terms

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500