recursive formula for geometric sequence

Use the nth term formula to write an equation.įormula for nth term, a n= a 1⋅ r ( n-1).Įxample 5. Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, …. The formula for the nth term isĮxample 4: Write an Equation for the nth Term We obtain the ratio by dividing a term by the term preceding it:Įach term after the first is obtained by multiplying the preceding term by -½. Soīecause each term after the first is ⅓ of the term preceding it, the nth term is given byįind a formula for the nth term of the geometric sequence We can obtain the common ratio by dividing any term after the first by the term preceding it. Write a formula for the nth term of the geometric sequence The first term and the common ratio determine all of the terms of a geometric sequence. (10) Substitute the values of r and a into the general formula to find the second expression for the nth term of the sequence. (Note that the value of a is the same for both values of r.) (9) Substitute the value of r into either of the two equations, say equation, and solve for a. (8) Now consider the negative value of r. (7) Substitute the values of r and a into the general equation to find the expression for the nth term. Substitute the value of r into either of the two equations, say equation, and solve for a. (6) Because there are two solutions, we have to perform two sets of computations. (4) Solve the equations simultaneously: divide equation by equation to eliminate a. (3) Similarly, use information about the seventh term to form an equation. (2) Use the information about the fifth term to form an equation. (1) Write the general rule for the nth term of a geometric sequence. Find the common ratio, r, the first term, a, and the nth term for the sequence. The fifth term in a geometric sequence is 14 and the seventh term is 0.56. (6) Find the 10th term by substituting n=10 into each of the two expressions for the nth term. Because there are two possible values for r, you must show both expressions for the nth term of the sequence. (5) Substitute the values of a and r into the general equation. (4) Solve for r (note that there are two possible solutions) (3) Substitute all known values into the general formula. (2) State the value of a (the first term in the sequence) and the value of the third term. (1) Write the general formula for the nth term in the geometric sequence. (7) Substitute the values of a and r into the general formula.įind the nth term and the 10th term in the geometric sequence where the first term is 3 and the third term is 12. (5) Write the general formula for the nth term of the geometric sequence. (4) Because the sequence is geometric, find the fourth term by multiplying the preceding (third) term by the common ratio. The sequence is geometric with the common ratio r=3. (3) Compare the ratios and make your conclusion. If it is geometric find the next term in the sequence, t 4, and the nth term for the sequence, t n. State whether the sequence t n: is geometric by finding the ratio of successive terms. ∴ the sequence is geometric with u 1=8 and r=½. Consider the sequence 8, 4, 2, 1, ½, …Ĭ) Hence, find the 12th term as a fraction.Ĭonsecutive terms have a common ratio of ½.

Hence, term number n, the power of r is one less than the term number ( n-1).įor a geometric sequence with first term u 1 and common ratio r, the general term or nth term is u n= u 1⋅ r ( n-1).Įxample 1. Then u 2= u 1 r, u 3= u 1⋅ r 2, u 4= u 1⋅ r 3, and so on. The sum of the geometric progression is S.Suppose the first term of a geometric sequence is u 1 and the common ratio is r. the nth term to be found in the sequence is a n

the first number of the geometric progression is a

The formulas applied by this geometric sequence calculator are detailed below while the following conventions are assumed: In mathematics, a geometric progression is also known as geometric sequence and represents a sequence of numbers (sequence being an ordered list of numbers) with the particularity that each member/term excepting the first one is found by multiplying the previous one by a fixed, non-zero number generally called the common ratio.įor example, the sequence 2, 10, 50, 250, 1250, 6250, 31250, 156250, 781250 is a geometric progression with the common ratio being 5. How does this geometric sequence calculator work?

Recursive formula for geometric sequence