Th Write an explicit formula for ans then term of the sequence 40,50,60, ....

Mathematics

1 answer:

kenny6666 [7]3 years ago

6 0

<h3>Answer: $a_n = 10n+30$ </h3>

n starts at 1, and n is a positive whole number (1,2,3,...)

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Explanation:

The sequence is arithmetic with first term 40 and common difference 10. Meaning we add 10 to each term to get the next one.

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a1 = 40 = first term

d = 10 = common difference

$a_n = a_1 + d(n-1)\\\\a_n = 40 + 10(n-1)\\\\a_n = 40 + 10n-10\\\\a_n = 10n + 30\\\\$

is the general nth term of this arithmetic sequence

Plug in n = 1 and you should get $a_1 = 40$

Plug in n = 2 and you should get $a_2 = 50$

and so on

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What is your sister’s total cost under each of the two plans?2. Suppose your sister doubles her monthly usage to 3,500 minutes a

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Answer:

(1) The total cost under Plan A is $92 and the total cost under Plan B is $515.

(2) The total cost under Plan A is $92 and the total cost under Plan B is $1,030.

Step-by-step explanation:

The question is incomplete, so the complete question is below:

$A\ cell \ phone \ company\ offers\ two \ different \ plans.$

$Plan\ A\ costs\ \$92\ per\ month\ for\ unlimited\ talk\ and\ text.\ Plan\ B\ costs \ $0.20\ per\ minute\ plus\ \$0.10\ per\ text\ message\ sent.$ $You\ need \ to\ purchase \ a \ plan \ for\ your \ 14-year-old \ sister$ $.Your\ sister\ currently \ uses\ 1,750 \ minutes\ and \ sends\ 1,650 \ texts\ each \ month.$ $(1) What\ is\ your \ sister's\ total\ cost\ under \ each\ of\ the\ two\ plans?$

$(2) Suppose\ your\ sister\ doubles\ her\ monthly\ usage \ to\ 3,500\ minutes \ and\ sends\ 3,300 \ texts.$ $What \ is \ your \ sister's \ total \ cost \ under \ each \ of \ the \ two \ plans?$

Now, to find (1) total cost for each of the two plans. (2) Total cost under each of the two plans, if sister doubles her monthly usage to 3,500 minutes and sends 3,300 texts.

As, the Plan A is for unlimited talk and text

Cost of the Plan A = $92.

Now, to find the cost under Plan B:

According to question:

Rate of call per minute is $0.20 and per text is $0.10.

Calls she uses currently is 1,750 minutes and text 1,650.

So, to get the cost of Plan B:

$0.20\times 1750+0.10\times 1650$