The equation for nth term of the arithmetic sequence: [tex]a_n = \frac{1}{7} + (n - 1)\frac{1}{7}[/tex]
The value of [tex]a_{10}[/tex] is [tex]\frac{10}{7}[/tex]
Solution:
Given that arithmetic sequence is:
[tex]\frac{1}{7} , \frac{2}{7} , \frac{3}{7} , \frac{4}{7} , .......[/tex]
To find: Equation for the nth term of the arithmetic sequence and [tex]a_{10}[/tex]
The formula for finding nth term in arithmetic sequence is given as:
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]a_n[/tex] = the nᵗʰ term in the sequence
[tex]a_1[/tex] = the first term in the sequence
d = the common difference between consecutive terms
common difference between consecutive terms = [tex]\frac{2}{7} - \frac{1}{7} = \frac{1}{7}[/tex]
Here first term [tex]a_1 = \frac{1}{7}[/tex]
Finding [tex]a_{10}[/tex]
[tex]a_{10} = \frac{1}{7} + (10 - 1) \frac{1}{7}\\\\a_{10} = \frac{1}{7} + 9 \times \frac{1}{7}\\\\a_{10} = \frac{1}{7} + \frac{9}{7}\\\\a_{10} = \frac{10}{7}[/tex]
Thus the equation for nth term of the arithmetic sequence:
[tex]a_{n}=a_{1}+(n-1)d\\\\a_n = \frac{1}{7} + (n - 1)\frac{1}{7}[/tex]
