Question

Write the six terms of each arithmetic sequencePlease see picture for question

Answer 1

The six terms for the arithmetic sequence is 1.6, 1.2, 0.8. 0.4, 0, -0.4

Step-by-step explanation

Given that;

`\begin{gathered} a_n\text{ = a}_{n\text{ - 1}}\text{ - 0.4} \\ \text{ a}_1\text{ = 1.6} \end{gathered}`

To find the second term, let n = 2

`\begin{gathered} \text{ a}_2\text{ }=\text{ a}_{2\text{ - 1}}\text{ - 0.4} \\ \text{ a}_2\text{ }=\text{ a}_1\text{ - 0.4} \\ \text{ a}_1\text{ = 1.6} \\ \text{ a}_2\text{ }=\text{ 1.6 - 0.4} \\ \text{ a}_2\text{ }=\text{ 1.2} \end{gathered}`

To find the third term, let n = 3

`\begin{gathered} \text{ a}_3\text{ }=\text{ a}_{3\text{ - 1}}\text{ - 0.4} \\ \text{ a}_3\text{ }=\text{ a}_2\text{ - 0.4} \\ \text{ a}_2\text{ = 1.2} \\ \text{ a3 }=\text{ 1.2 - 0.4} \\ \text{ a}_3\text{ = 0.8} \end{gathered}`

To find the fourth term, let n = 4

`\begin{gathered} \text{ a}_4\text{ }=\text{ a}_{4-\text{ 1}}\text{ - 0.4} \\ \text{ a}_4\text{ = a}_3\text{ - 0.4} \\ \text{ a}_3\text{ = 0.8} \\ \text{ a}_4\text{ = 0.8 - 0.4} \\ \text{ a}_4\text{ = 0.4} \end{gathered}`

To find the fifth term, let n = 5

`\begin{gathered} \text{ a}_5\text{ = a}_{5\text{ - 1}}\text{ - 0.4} \\ \text{ a}_5\text{ }=\text{ a}_4\text{ - 0.4} \\ \text{ a}_4\text{ = 0.4} \\ \text{ a}_5\text{ = 0.4 - 0.4} \\ \text{ a}_5\text{ = 0} \end{gathered}`

To find the 6th term, let n = 6

`\begin{gathered} \text{ a}_6\text{ }=\text{ a}_{6\text{ - 1}}\text{ - 0.4} \\ \text{ a}_6\text{ = a}_5\text{ - 0.4} \\ \text{ a}_5\text{ = 0} \\ \text{ a}_6\text{ = 0 - 0.4} \\ \text{ a}_6\text{ = -0.4} \end{gathered}`

Hence, the six terms for the arithmetic sequence is 1.6, 1.2, 0.8. 0.4, 0, -0.4