In this sequence, term number 1 has a value of 6,
term number 2 has a value of 12, term number 3 has
a value of 22, and so on:
6, 12, 22, 36, 54,
if n represents the term number, demonstrate that
the rule 2n + 4 will generate the sequence.

2n² + 4

Step-by-step explanation:

Let, ...... (1)

Now, sift the right hand side by one term and subtract from original equation (1).

Hence, we get  

(

⇒ tₙ = 6 + [ 6 + 10 + 14 + 18 + ........ up to (n-1)th term]  

Now, the sum within the bracket is an A.P. sum.

Hence, tₙ = 6+ []

               = 6+

               = 6+ 2(n²-1)

                = 2n² + 4

Therefore, the general term 2n² + 4 represent the sequence. (Answer)

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40