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Find Specified Terms of Arithmetic and Geometric Sequences

$Find\ the\ 10^{th}\ term\ of\ the\ sequence\ 2,\ 5,\ 8,\ 11,\ ...$

arithmetic: difference between terms is an additive constant

geometric: difference between terms is a multiplicative constant

Check A: 5 – 3 = 3

8 – 5 = 3

11 – 8 = 3

$10^{th}\ term=\ 29$

$Find\ the\ 6^{th}\ term\ of\ the\ sequence\ \frac{3}{4},\ \frac{3}{2},\ 3,\ 6,\ ...$

Check A:

$\frac{3}{2} -\frac{3}{4} =\frac{6}{4} -\frac{3}{4} =\frac{3}{4}$

$3-\frac{3}{2} =\frac{6}{2} -\frac{3}{2} =\frac{3}{2}$

Check G:

$\frac{3}{2}\div\frac{3}{4} =\frac{3}{2}\times\frac{4}{3} =\frac{4}{2} =2$

$3\div\frac{3}{2} =3\times\frac{3}{2} =2$

$6\div 3=2$

$6^{th}\ term=24$