Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $$\mathbf { a } _ { \mathbf { n } }$$ to find $$a _ { 20 }$$ , the 20th term of the sequence.
-To train for a race, Will begins by jogging 14 minutes one day per week. He increases his jogging time by 4 minutes each week. Write the general term of this arithmetic sequence, and find how many whole weeks it takes for him to reach a jogging time of one hour.
A) $a _ { n } = 4 n + 10 ; 13$ weeks
B) $a _ { n } = 4 n + 14 ; 12$ weeks
C) $a _ { n } = 4 n + 10 ; 12$ weeks
D) $a _ { n } = 4 n + 14 ; 13$ weeks

Question

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $$\mathbf { a } _ { \mathbf { n } }$$ to find $$a _ { 20 }$$ , the 20th term of the sequence.
-To train for a race, Will begins by jogging 14 minutes one day per week. He increases his jogging time by 4 minutes each week. Write the general term of this arithmetic sequence, and find how many whole weeks it takes for him to reach a jogging time of one hour. 
A) $a _ { n } = 4 n + 10 ; 13$ weeks
B) $a _ { n } = 4 n + 14 ; 12$ weeks
C) $a _ { n } = 4 n + 10 ; 12$ weeks
D) $a _ { n } = 4 n + 14 ; 13$ weeks

Quizplus · Accepted Answer

The general term of the arithmetic sequence is $a _ { n } = 4 n + 10$. To find the 20th term, substitute $n = 20$ into the formula: $a _ { 20 } = 4 ( 20 ) + 10 = 90$ minutes. To find how many whole weeks it takes for Will to reach a jogging time of one hour, solve the equation $a _ { n } = 60$: $4 n + 10 = 60$, which gives $n = 12$ weeks.

Write a Formula for the General Term (The Nth Term) an\mathbf { a } _ { \mathbf { n } }an​

Write a Formula for the General Term (The Nth Term) $\mathbf { a } _ { \mathbf { n } }$