In this lesson, it is assumed that you know what an arithmetic sequence is and can find a common difference. Notice this example required making use of the general formula twice to get what we need.
If we simplify that equation, we can find a1. When writing the general expression for a geometric sequence, you will not actually find a value for this. The explicit formula is also sometimes called the closed form. To find the explicit formula, you will need to be given or use computations to find out the first term and use that value in the formula.
Notice that the an and n terms did not take on numeric values. Find the explicit formula for 0. Find the recursive formula for 0. Find the explicit formula for 5, 10, 20, 40. Order of operations tells us that exponents are done before multiplication.
In this situation, we have the first term, but do not know the common ratio. For example, when writing the general explicit formula, n is the variable and does not take on a value. DO NOT multiply the 2 and the 3 together. To find the 10th term of any sequence, we would need to have an explicit formula for the sequence.
Rather than write a recursive formula, we can write an explicit formula. This is enough information to write the explicit formula.
Find the explicit formula for a geometric sequence where and. But if you want to find the 12th term, then n does take on a value and it would be This geometric sequence has a common ratio of 3, meaning that we multiply each term by 3 in order to get the next term in the sequence. So the explicit or closed formula for the geometric sequence is.
Find a6, a9, and a12 for problem 4. If we do not already have an explicit form, we must find it first before finding any term in a sequence.
This sounds like a lot of work. However, the recursive formula can become difficult to work with if we want to find the 50th term. This will give us Notice how much easier it is to work with the explicit formula than with the recursive formula to find a particular term in a sequence.
What happens if we know a particular term and the common ratio, but not the entire sequence? You will either be given this value or be given enough information to compute it.
Your formulas should be simplified if possible, but be very careful when working with exponential expressions. To write the explicit or closed form of a geometric sequence, we use anis the nth term of the sequence.
There must be an easier way. So 3 must be raised to the power as a separate operation from the multiplication. Using the recursive formula, we would have to know the first 49 terms in order to find the 50th.
You must substitute a value for r into the formula. Now we use the formula to get Notice that writing an explicit formula always requires knowing the first term and the common ratio.
Find a6, a9, and a12 for problem 8. Find a6, a9, and a12 for problem 6. Now that we know the first term along with the r value given in the problem, we can find the explicit formula. Site Navigation Geometric Sequences This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence.
We have r, but do not know a1.(2) The table contains more than two pairs of values, but still exactly linear, looking for a function of the form y = mx + c. (3) The table contains several pairs of exact values, with an expected answer being a simple polynomial function, an exponential function or some other simple function (e.g.
sinusoid). home / study / math / prealgebra / prealgebra questions and answers / Write An Expression For The Sequence In The Table. Question: Write an expression for the sequence in the table.
Show transcribed image text Write an expression for the sequence in the table. write an expression for the nth term of the sequence 0, 7, 16, 27, 40 It is neither geometric or arithmetic My teacher gave us a key and I can't read his writing please any help would be great!!
Feb 08, · Write an algebraic expression for the nth term of the table below A: 0 1 2 3 4 5 n B: 3 5 7 9 11 13? Please show work note: i hate these tables:p i cant figure them Status: Resolved.
Improve your math knowledge with free questions in "Write variable expressions for arithmetic sequences" and thousands of other math skills. Free Sequences calculator - find sequence types, indices, sums and progressions step-by-step.Download