# How do you write a rule for the nth term of the arithmetic sequence and then find #a_10# for #d=5, a_5=33#?

By signing up, you agree to our Terms of Service and Privacy Policy

To write a rule for the nth term of an arithmetic sequence, you can use the formula: ( a_n = a_1 + (n - 1) \times d ), where ( a_n ) is the nth term, ( a_1 ) is the first term, ( n ) is the term number, and ( d ) is the common difference.

Given ( a_5 = 33 ) and ( d = 5 ), first find ( a_1 ) by substituting the values into the formula. Then, use the same formula to find ( a_{10} ) by substituting ( n = 10 ) and the found value of ( a_1 ).

Step 1: Substitute ( a_5 = 33 ) and ( d = 5 ) into the formula to find ( a_1 ): [ a_5 = a_1 + (5 - 1) \times 5 ] [ 33 = a_1 + 4 \times 5 ] [ 33 = a_1 + 20 ] [ a_1 = 33 - 20 ] [ a_1 = 13 ]

Step 2: Use the formula to find ( a_{10} ) with ( n = 10 ): [ a_{10} = 13 + (10 - 1) \times 5 ] [ a_{10} = 13 + 9 \times 5 ] [ a_{10} = 13 + 45 ] [ a_{10} = 58 ]

Therefore, ( a_{10} = 58 ) for the given arithmetic sequence.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the sum of the terms of the series 4+7+10+.....+22?
- Is 10, 5, 2.5, 1.25, 0.625, 0.3125 a geometric sequence?
- How do I find the common ratio of a geometric sequence?
- The 15th term of an arithmetic series is 52, and the sum of the first 15 terms is 405 how do you find the sum of the first 22 terms?
- How do you write the expression for the nth term of the sequence given #3, 7, 11, 15, 19,...#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7