1. Find the 16th term of the sequence 9, 16, 23, 30. The sequence is arithmetic with first term $a_1=9$ and common difference $d=16-9=7$. The formula for the $n$th term is $$a_n = a_1 + (n-1)d$$ Calculate the 16th term: $$a_{16} = 9 + (16-1) \times 7 = 9 + 15 \times 7 = 9 + 105 = 114$$ 2. Find the 25th term of the sequence 16, 20, 24, 28. Here, $a_1=16$, $d=20-16=4$. $$a_{25} = 16 + (25-1) \times 4 = 16 + 24 \times 4 = 16 + 96 = 112$$ 3. Find the 100th term of the sequence 19, 26.5, 34, 41.5. $a_1=19$, $d=26.5-19=7.5$. $$a_{100} = 19 + (100-1) \times 7.5 = 19 + 99 \times 7.5 = 19 + 742.5 = 761.5$$ 4. Find the 19th term of the sequence 7, 14, 21, 28, 35, 42. $a_1=7$, $d=14-7=7$. $$a_{19} = 7 + (19-1) \times 7 = 7 + 18 \times 7 = 7 + 126 = 133$$ 5. Find the 14th term of the sequence 5, 11, 17, 23, 29, 35. $a_1=5$, $d=11-5=6$. $$a_{14} = 5 + (14-1) \times 6 = 5 + 13 \times 6 = 5 + 78 = 83$$ 6. Find the 13th term of the sequence 7, 1, -5, -11, -17, -23. $a_1=7$, $d=1-7=-6$. $$a_{13} = 7 + (13-1) \times (-6) = 7 + 12 \times (-6) = 7 - 72 = -65$$ 7. Find the 11th term of the sequence -7, 1, 9, 17, 25, 33. $a_1=-7$, $d=1-(-7)=8$. $$a_{11} = -7 + (11-1) \times 8 = -7 + 10 \times 8 = -7 + 80 = 73$$ 8. Find the 13th term of the sequence -0.9, -1.9, -2.9, -3.9, -4.9, -5.9. $a_1=-0.9$, $d=-1.9 - (-0.9) = -1$. $$a_{13} = -0.9 + (13-1) \times (-1) = -0.9 + 12 \times (-1) = -0.9 - 12 = -12.9$$ 9. The second term is 13 and the sixth term is 41. Find the tenth term. Let $a_1$ be the first term and $d$ the common difference. From $a_2 = a_1 + d = 13$ and $a_6 = a_1 + 5d = 41$. Subtracting: $$a_6 - a_2 = (a_1 + 5d) - (a_1 + d) = 4d = 41 - 13 = 28$$ So, $$d = \frac{28}{4} = 7$$ Then, $$a_1 + d = 13 \Rightarrow a_1 + 7 = 13 \Rightarrow a_1 = 6$$ Find the 10th term: $$a_{10} = a_1 + 9d = 6 + 9 \times 7 = 6 + 63 = 69$$