Question

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

Answer 1

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

Answer 2

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