Question

Write the first 5 terms In the sequence. Ps solve both pls

Answer 1

Question 4

Step 1:

Write the nth term equation or formula

`a_n=a_(n-1)\text{ - }\sqrt[]{5}`

Step 2:

`\begin{gathered} To\text{ find } \\ a_2,\text{ substitute n = 2 } \\ a_2=a_(2-1)\text{ - }\sqrt[]{5} \\ \text{ = a}_1\text{ - }\sqrt[]{5} \\ =\text{ 2}\sqrt[]{5}\text{ - }\sqrt[]{5} \\ a_2\text{ = }\sqrt[]{5} \end{gathered}`
`\begin{gathered} a_3=a_(3-1)\text{ - }\sqrt[]{5} \\ =a_2\text{ - }\sqrt[]{5} \\ =\text{ }\sqrt[]{5}\text{ - }\sqrt[]{5} \\ a_2=\text{ 0} \end{gathered}`
`\begin{gathered} a_4=a_(4-1)\text{ - }\sqrt[]{5} \\ =a_3\text{ - }\sqrt[]{5} \\ =\text{ 0 - }\sqrt[]{5} \\ a_4\text{ = -}\sqrt[]{5} \end{gathered}`
`\begin{gathered} a_5=a_(5-1)\text{ - }\sqrt[]{5} \\ =a_4\text{ - }\sqrt[]{5} \\ =\text{ -}\sqrt[]{5}\text{ - }\sqrt[]{5} \\ a_5=\text{ -2}\sqrt[]{5} \end{gathered}`
`\begin{gathered} \text{The first five terms are:} \\ 2\sqrt[]{5},\text{ }\sqrt[]{5}\text{ , 0 , -}\sqrt[]{5}\text{ , -2}\sqrt[]{5} \end{gathered}`

Question 6

`\begin{gathered} a_n=a_(n-1)\text{ - 2} \\ a_1\text{ = -1} \end{gathered}`
`\begin{gathered} a_2=a_(2-1)\text{ - 2} \\ =a_1\text{ - 2} \\ a_2=\text{ -1 -2 = -3} \\ a_3=a_(3-1)-2_{} \\ =a_2\text{ - 2} \\ =\text{ -3 -2 } \\ a_3\text{ = -5} \\ a_4=a_(4-1)\text{ - 2} \\ =a_3\text{ - 2} \\ =\text{ -5 - 2 } \\ a_4\text{ = -7} \\ a_5=a_(5-1)\text{ - 2} \\ a_5=a_4\text{ - 2} \\ a_5\text{ = -7 - 2} \\ a_5\text{ = -9} \end{gathered}`

Final answer

First five terms:

-1 , -3 , -5, -7 , -9