Question

Find the 10th term of an arithmetic sequence sequence if t1=2.1 and t4=1.83

Answer 1

Step 1: Concept

Write the nth term formula for an arithmetic sequence.

`\begin{gathered} T_n\text{ = a + (n - 1 ) d} \\ a\text{ = first term} \\ n\text{ = number of term} \\ d\text{ = common difference} \\ T_n\text{ = nth term} \end{gathered}`

Step 2: List the given data

`\begin{gathered} t_1\text{ = 2.1 a = 2.1} \\ T_4\text{ = 1.83} \\ d\text{ = ?} \end{gathered}`

Step 3: Find the common difference.

To find the common difference, you substitute the given values.

`\begin{gathered} T_4\text{ = a + (n - 1)d} \\ 1.83\text{ = 2.1 + (4 - 1) d} \\ \text{Collect like term} \\ 1.83\text{ - 2.1 = 3d} \\ -0.27\text{ = 3d} \\ \text{Next, divide both through 3} \\ (-0.27)/(3)\text{ = }(3d)/(3) \\ d\text{ = -0.09} \end{gathered}`

Step 4: Find the 10th term.

Final answer

`\begin{gathered} \text{Substitute the values of a = 2.1, d = -0.09 and n = 10 to find the 10th} \\ \text{term} \\ \text{Therefore} \\ T_{n\text{ }}=\text{ a + (n - 1)d} \\ T_(10)\text{ = 2.1 + (10 - 1) x (-0.09)} \\ =\text{ 2.1 + (9)(-0.09)} \\ =\text{ 2.1 - 0.81} \\ =\text{ 1.19} \end{gathered}`

The 10th term = 1.19