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explain how the number of text messages Dario sent and the cost form an arithmetic sequence. Then write an expression to find Dario's text messaging bill if he sends N text messages over 250

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HomertheGenius

For less than or equal to 250 text messages Dario pays $5.00. After that, for every additional text message he pays $0.15.It means that the number of additional text messages ( n = 1, 2, 3, ... ) and the cost: ( c1 = $5.15,  c2 = $5.30,  c3 = $5.45, ... ) form an arithmetic sequence.An expression for the bill Dario must pay if he sends more than 250 text messages is:C = 5.00 + n · 0.15For example, if he has 260 text messages: 260 - 250 = 10C (260) = 5.00 + 10 · 0.15 = 5.00 + 1.50 = $6.50  

Answer:

Step-by-step explanation:

Given that upto 250 messages Dario sent there is a fixed rate say C=5

i.e. even if Dario sends 1 message Dario has to pay C

After 250 messages for each additional message 0.15 has to be paid

This means for 251 , 5.15

252, 5.30

253, 5.45 and so on.

Hence this forms an arithmetic sequence with starting at 5 and common difference 0.15

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