How many terms has the GP whose 2nd term is 1/2 and the common ratio and the last term are 1/4 and 1 128 respectively?

There are five terms in this Geometric Progression. if 1/2 is the second term and the ratio is 1/4, the first term must be 2. hence n=5 which means the number of terms in the series is 5.

What is the common ratio of a geometric sequence whose first term is 12 and its fourth term is 768?

Explanation: The general form of a geometric sequence with the first term a is a,ar,ar2,ar3,… where r is the common ratio between terms. Note that the general form for the n th term is arn−1 .

How do you find the common ratio?

You can determine the common ratio by dividing each number in the sequence from the number preceding it. If the same number is not multiplied to each number in the series, then there is no common ratio.

What is the common ratio of the geometric sequence?

2
The common ratio is the number you multiply or divide by at each stage of the sequence. The common ratio is therefore 2. You can find out the next term in the sequence by multiplying the last term by 2.

What is common ratio in GP?

In geometric progression, the common ratio is the ratio between any one term in the sequence and divide it by the previous term. Usually, it is represented by the letter “r”.

How do you calculate common ratio in GP?

To calculate the common ratio of a GP, divide the second term of the sequence with the first term or simply find the ratio of any two consecutive terms by taking the previous term in the denominator.

What is the formula of common ratio in GP?

Geometric Progression The nth term of a GP series is Tn = arn-1, where a = first term and r = common ratio = Tn/Tn-1) . The sum of infinite terms of a GP series S∞= a/(1-r) where 0< r<1. If a is the first term, r is the common ratio of a finite G.P.

How do you find the sum of the terms of GP?

The formula to find sum of n terms of GP is: Also, if the common ratio is equal to 1,then the sum of the GP is given by: a, ar, ar 2, ar 3 ,……ar n-1 is called finite geometric series. The sum of finite Geometric series is given by: Terms of an infinite G.P. can be written as a, ar, ar 2, ar 3, ……ar n-1 ,…….

What is the formula for the general form of a GP?

Geometric Progression Formulas The general form of terms of a GP is a, ar, ar2, ar3, and so on. Here, a is the first term and r is the common ratio. The nth term of a GP is Tn = arn-1 Common ratio = r = Tn/ Tn-1 The formula to calculate the sum of the first n terms of a GP is given by: Sn = a [

How do you find the common ratio of a geometric sequence?

Find the common ratio of a Geometric Sequences. The common ratio, r, is found by dividing any term after the first term by the term that directly precedes it. In the following examples, the common ratio is found by dividing the second term by the first term, a 2/a 1 .

What is the formula to find the nth term of GP?

Therefore, the formula to find the nth term of GP is: a n = ar n-1 Note: nth term is the last term of GP.