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Mathematical explorations classroomready activities Visualizing Algebraic Rules for the nth Term d Christine A. Perry and Vivian F. Cyrus Determining an algebraic expression to generalize a pattern.

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In this case, the nth term = 2n. To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 = 8. What is the nth term of the sequence 2, 5, 10, 17, 26... ? This is the required sequence, so the nth term is n² + 1.

To work out the nth term, we first must work out the common difference, and then we look at how we make the common difference equal one of the terms in the sequence. Usually, it will look something like "n+1", or "3n-5". For example, work out the nth term for the linear sequence "2, 5, 8, 11, ...".

0:03 1:48 Suggested clip Write the nth term rule for a geometric sequence - YouTubeYouTubeStart of suggested clipEnd of suggested clip Write the nth term rule for a geometric sequence - YouTube

The 'nth' term is a formula with 'n' in it which enables you to find any term of a sequence without having to go up from one term to the next. 'n' stands for the term number so to find the 50th term we would just substitute 50 in the formula in place of 'n'.

The nth term of a geometric sequence is a r n 1 , where is the first term and is the common ratio.

The expression for the total number of tiles in the nth term is the sum of the areas of the rectangles, n2 + n(n 1) + 2, which can be simpli- fied to 2n2 n + 2. quadratic sequences with visual models.

It can be calculated by dividing any term of the geometric sequence by the term preceding it. Identify the number of term you wish to find in the sequence. Call this number n. For example, if you wish to find the 8thterm in the sequence, then n = 8.

2:19 8:44 Suggested clip Geometric Sequences | Determine the nth term - YouTubeYouTubeStart of suggested clipEnd of suggested clip Geometric Sequences | Determine the nth term - YouTube

First let n=10, a1=1, a10=4 and use the formula an=a1 r(n-1) to find r. Now use the formula an=a1 r(n-1) again, this time with n=17. Again, a is the first term and r is the ratio. Remember that a1 r(n-1) (a1 r)(n-1).

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