Write a formula for the nth term of the arithmetic sequence 15, 20, 25, 30, ...

Question
Sequences
asked 2021-02-09
Write a formula for the nth term of the arithmetic sequence 15, 20, 25, 30, ...

Answers (1)

2021-02-10
The nnth term of an arithmetic sequence is \(a_{n} = a_{1}+(n-1)d\) where a_1is the first term and d is the common difference.
For the arithmetic sequence 15, 20, 25, 30, ... the first term is \(a_{1} = 15\) and the common difference is \(d = a_{2} - a_{1} = 20-15 = 5\). The nth term is then:
\(a_{n} = a_{1}+(n - 1)d\)
\(a_{n} = 15 + (n - 1)(5)\\) Substitute.
\(a_{n} = 15 +5n-5\\) Distribute.
\(a_{n} = 10 + 5n\) Combine like terms.
0

Relevant Questions

asked 2020-11-26
WRITE A RULE FOR THE nth TERM OF THE ARITHMETIC SEQUENCE THEN FIND a_25: {1.6,4,6.4,8.8,11.2,…} *
asked 2020-12-05
Several terms of a sequence {a_n}_(n=1)^oo are given. a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of the sequence). c. Find an explicit formula for the nth term of the sequence. {1, 3, 9, 27, 81, ...}
asked 2021-03-08
A soup kitchen makes 16 gallons of soup. Each day, a quarter of the soup is served and the rest is saved for the next day. Write the first five terms of the sequence of the number of fluid ounces of soup left each day. Write an equation that represents the nth term of the sequence. When is all the soup gone?
asked 2021-01-27
Find the nth term of the sequence 2, 5, 10,17, 26...
asked 2021-02-19
Write a recursive rule and an explicit rule for an arithmetic sequence that models a situation. Then use the rule to answer the question. Jack begins an exercise routine for 10 minutes each day. Each week he plans to add 10 minutes per day to his exercise routine. For how many minutes will he exercise for each day on the 7th week?
asked 2021-02-25
What is an arithmetic sequence? Write a formula for the nth term of an arithmetic sequence.
asked 2020-11-01
Write the recursive formula for each geometric sequence. 640, 160, 40, 10, 2.5, ...
asked 2020-12-03
1. Is the sequence \(0.3, 1.2, 2.1, 3, ...\) arithmetic? If so find the common difference.
2. An arithmetic sequence has the first term \(a_{1} = -4\) and common difference \(d = - \frac{4}{3}\). What is the \(6^{th}\) term?
3. Write a recursive formula for the arithmetic sequence \(-2, - \frac{7}{2}, -5, - \frac{13}{2} ...\) and then find the \(22^{nd}\) term.
4. Write an explicit formula for the arithmetic sequence \(15.6, 15, 14.4, 13.8, ...\) and then find the \(32^{nd}\) term.
5. Is the sequence \(- 2, - 1, - \frac{1}{2},- \frac{1}{4},...\) geometric? If so find the common ratio. If not, explain why.
asked 2020-11-09
the sum of the first 8 terms of a geometric sequence is 6560. The common ratio is 3. What is the third term of the sequence?
asked 2020-12-24
The first of an arithmetic sequence is 2 and has the property that its second, third, and seventh terms are consecutive terms of a geometric sequence.
...