Question

Wire the explicit expression that can be used to find the nth term in this sequence 3,7,11,15,19An = What would be the 20th term A20 =

Answer 1

From the sequence given 3,7,11,15,19

first term (a) = 3

common difference(d) = 4

Hence to find the nth term, the expression is given as shown below

`\begin{gathered} T_n\text{ = a + (n -1)d} \\ T_n\text{ = 3 + (n - 1)4} \\ \text{ = 3 + 4n -4} \\ \text{ = 4n - 4+ 3} \\ \text{ = 4n - 1} \end{gathered}`

To find the 20th term, we have

`\begin{gathered} T_n\text{ = a + (n -1)d} \\ a\text{ = 3, d = 4},\text{ n = 20} \\ T_n\text{ = a + (n -1)d} \\ T_n\text{ = 3 + (20 - 1)4} \\ T_(20)\text{ = 3 + (19)4 } \\ T_(20)\text{ = 3 +76} \\ T_(20)\text{ = 79} \end{gathered}`