write a variable expression to describe the rule for the sequence. Then find the 10th term. 15,13,11, 9..

The variable expression to describe the rule of sequence is [tex]T_{n}=17-2 n[/tex] And the 10th term is -3 Solution:The given series is 15, 13, 11, 9 …. The given series is arithmetic series with common difference "-2"From the above series we get,First term [tex]a_1 = 15[/tex]Second term [tex]a_2 = 13[/tex]And so on.Common difference = [tex]d = a_2 - a_1 = -2[/tex]The nth term of Arithmetic progression is given as:[tex]\mathrm{T}_{\mathrm{n}}=\mathrm{a}_{1}+(\mathrm{n}-1) \mathrm{d}[/tex]Where "a" is the first term of sequence"n" is the nth term"d" is common difference between terms[tex]\begin{array}{l}{T_{n}=15+(n-1) \times(-2)} \\\\ {T_{n}=15-2 n+2} \\\\ {T_{n}=17-2 n}\end{array}[/tex]Which is the required variable expression to describe the rule for the given sequenceFinding 10th term:Substitute n = 10 in above variable expressi[tex]T_{10} = 17 - 2(10) = 17 - 20 = -3[/tex]Hence the 10th term is -3