a. Start with 2, and then add 3, just like it asks. So: \(2+3=5\) and then \(5+3 = 8\) and so on to give, 2,5,8,11,14.
b.For each term number we add one less than that many '3's to it. I.E. for the first term we add zero '3's for the second we add one and so on. This pattern is written as \(T_n = 2+3(n-1)\) which means we start with 2 and add 3 over and over. For the sixth term we repalce n with 6: \(T_{6} = 2+(3*5)\)
c. For the sixth term we just evaluate out patterna bove and get 17. We can check this by follwoing out 'add three' pattern: 14+3=17, same as above.
2. a. Start with 5, and then add 5, just like it asks. So: 5+5=10; 10+5=15 and so on, to get: 5,10,15,20,25
b. Same as above, start with what they give you, ten keep adding what they tell you untill you have enough terms 20+20=40; 40+20=60 and so on to get: 20,40,60,80,100
c. I cant draw a cirlce here but the paris are: 5 & 20, 10 & 40, 15 & 60, 20 & 80, 25 & 100.
d. In each pair, the botthom term is 4 times the top term. We can check this with a few examples: \(\frac{20}{5} = 4\); \(\frac{80}{20} = 4\). This works for all the pairs.
3. For each term the Cost in Dollars is 0.99 times the number of songs. i.e. A single song cost 99cents, two songs costs (2 * 99cents) and so on. You can check this for any number of songs by doing 0.99 times the number of songs. For example for 5 songs we have 5 * 0.99 = 4.95.
4. Using our pattern above (0.99 * number of songs) we get (0.99 * 6 songs = $5.94)
a. 2+3=5, 5+3=8, 8+3=11, 11+3=14, first 5 terms are 2,5,8,11,14
b. expression is 3n-1
c. 6th term is 17
2.a. 5+5=10, 10+5=15, 15+5=20, 20+5=25 first 5 terms are 5,10,15,20, 25 b. 20+20=40, 40+20=60, 60+20=80, 80+20=100 fisrt 5 terms are 20,40,60,80,100 c. corsponding is 20 d. coresonding is 20
3. cost=numberofsongs times 0.99 4. 0.99 times 6=cost=5.94
