Sure! Let's solve this step-by-step.
Given the sequence formula for the [tex]\( n \)[/tex]-th term:
[tex]\[ T_n = 3n - 10 \][/tex]
We are asked to find which term in this sequence equals 50. That is, we need to determine the value of [tex]\( n \)[/tex] for which:
[tex]\[ T_n = 50 \][/tex]
Substituting [tex]\( T_n \)[/tex] with 50 in the given sequence formula, we have:
[tex]\[ 50 = 3n - 10 \][/tex]
Next, we solve for [tex]\( n \)[/tex]:
1. Add 10 to both sides of the equation to isolate the term with [tex]\( n \)[/tex]:
[tex]\[ 50 + 10 = 3n \][/tex]
[tex]\[ 60 = 3n \][/tex]
2. Divide both sides by 3 to solve for [tex]\( n \)[/tex]:
[tex]\[ \frac{60}{3} = n \][/tex]
[tex]\[ 20 = n \][/tex]
So, the value of [tex]\( n \)[/tex] for which the term equals 50 is:
[tex]\[ n = 20 \][/tex]
Therefore, the 20th term of the sequence is 50.
