Arithmetic progression homework

Thread starter Michael_Light
Start date Mar 2, 2011
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Arithmetic Arithmetic progression Homework

In summary, an arithmetic progression is a sequence of numbers with a constant difference between consecutive terms. The common difference can be found by subtracting any two consecutive terms, and the formula for finding the nth term is an = a1 + (n-1)d. The sum of an arithmetic progression can be found using the formula Sn = (n/2)(a1 + an). It is possible for an arithmetic progression to have a negative common difference, resulting in decreasing terms.

Mar 2, 2011

Michael_Light

Homework Statement

Need help with number (9)..

Homework Equations

The Attempt at a Solution

Can anyone give me some hints? Thanks.

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Mar 3, 2011

tiny-tim

Science Advisor

Homework Helper

Think. Subtract.

Mar 19, 2011

Suk-Sci

S_n=3n² + 4n
Hint:
S₁=3+4=7
S₂=12+8=20

Related to Arithmetic progression homework

1. What is an arithmetic progression?

An arithmetic progression is a sequence of numbers where the difference between any two consecutive terms is constant. For example, in the sequence 2, 5, 8, 11, 14, the difference between each term is 3.

2. How do I find the common difference in an arithmetic progression?

The common difference in an arithmetic progression can be found by subtracting any two consecutive terms in the sequence. For example, in the sequence 2, 5, 8, 11, 14, the common difference is 5 - 2 = 3.

3. What is the formula for finding the nth term in an arithmetic progression?

The formula for finding the nth term in an arithmetic progression is:

a_n = a₁ + (n-1)d

Where a_n is the nth term, a₁ is the first term, and d is the common difference.

4. How do I determine the sum of an arithmetic progression?

The sum of an arithmetic progression can be found using the formula:

S_n = (n/2)(a₁ + a_n)

Where S_n is the sum of the first n terms, a₁ is the first term, and a_n is the nth term.

5. Can an arithmetic progression have a negative common difference?

Yes, an arithmetic progression can have a negative common difference. This means that the terms in the sequence will decrease by a constant amount instead of increasing.