The fifth term of an arithmetic sequence is 11 and the tenth term is 41. what is the first term?

In this sequence, the first term is and every successive term is determined by

where is the common difference between terms. We have

so that

Then

The first term is -13.

Step-by-step explanation:

The general rule of an arithmetic sequence is the following:

In which d is the common diference between each term.

This is the case going from one term to the next. However, when, as in this problem, we have the fifth and the tenth term, this formula can be expanded, as the following way:

So

The common diference is 6.

To find the first term, we do:

The first term is -13.

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