What is the rule to respresent this function?

Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified term number. 2+6+18+

Inessa [10]

The given series is a geometric series. The sum of its first 6 terms is 728.

To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.

If it is an arithmetic series, then:

a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric series, then:

a(n) = a(n-1) . r

where r is the common ratio.

The given series is:

2+6+18+ . . . .

and the number of terms is 6.

In the given series:

a(1) = 2

a(2) = 6

a(3) = 18

Notice that

a(2)/a(1) = 6/2 = 3

a(3)/a(2) = 18/6 = 3

Since the ratio of consecutive terms are constant, then the given series is a geometric series. Furthermore, its ratio, r = 3

Sum formula for the first n term of a geometric series is:

S(n) = a(1) . (rⁿ -1)/(r -1)

Substitute n = 6, a(1) = 2, and r = 3

S(6) = 2 . (3⁶ - 1)/(3 - 1)

S(6) = 2. 364

= 728

We can also evaluate the sum directly. Write all the terms until n = 6.

a(4) = 18 . 3 = 54

a(5) = 54 . 3 = 162

a(6) = 162 . 3 = 486

Hence, the series is:

2+6+18+54+162+486 = 728

Learn more about series here:

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7 0

1 year ago

Brenda can deliver 644 newspapers in 7 hour how many newspapers can brenda deliver in 9 hours

Naya [18.7K]

In 7 hours 644 newpapers
in one hour it is 644/7= 92
in 9 hours-> 92x9 =828 newspapers

6 0

3 years ago

How do i simplify this expression?

levacccp [35]

First, you try to make sure that both the denominators are the same. In order to do this, you multiply both fractions' numerator and denominator by the other fraction's denominator. Next, you combine like terms in the numerator, and then you simplify the fraction.

8 0

4 years ago

Exponential Function:

Alex73 [517]

Answer:

See below and attached

Step-by-step explanation:

Given functions

1. f(x) = 5*2ˣ