Sage-Tips

What type of sequence is 3/15 75?

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 5 gives the next term. In other words, an=a1⋅rn−1 a n = a 1 ⋅ r n – 1 . This is the form of a geometric sequence.

What is the sum of the geometric sequence 3/15 75 If there are 8 terms?

292968
The sum of the geometric sequence 3, 15, 75, …, if there are 8 terms, is S8 = 292968.

What is the next number in the pattern 2 12 72?

You can clearly see that the given sequence is a Geometric Progression (G.P.) with first term as 2 and common ratio as 6. So, we can say that each term is 6 times its previous term. So the next term of this sequence will be given by 6*432 which is equal to 2592 .

What is the sum of the infinite geometric sequence?

The formula for the sum of an infinite geometric series is S∞ = a1 / (1-r ).

How do you find the sum of the first 10 terms of a geometric sequence?

The formula to find the sum of the first n terms of a geometric sequence is a times 1 minus r to the nth power over 1 minus r where n is the number of terms we want to find the sum for, a our beginning term of our sequence, and r our common ratio.

What is the formula for the sum of the first n terms of a geometric series?

For r≠1 r ≠ 1 , the sum of the first n terms of a geometric series is given by the formula s=a1−rn1−r s = a 1 − r n 1 − r .

What kind of sequence is 6 18 54?

geometric sequence
A geometric sequence (also known as a geometric progression) is a sequence of numbers in which the ratio of consecutive terms is always the same. For example, in the geometric sequence 2, 6, 18, 54, 162, …, the ratio is always 3. This is called the common ratio.

How do you find the next number in the sequence?

The question states that the sequence is arithmetic, which means we find the next number in the sequence by adding (or subtracting) a constant term. We know two of the values, separated by one unknown value.

How do you find the common difference of a sequence?

Correct answer: First, find the common difference for the sequence. Subtract the first term from the second term. Subtract the second term from the third term. To find the next value, add to the last given number.

How do you add 7 to 36 in a sequence?

First, find a pattern in the sequence. You will notice that each time you move from one number to the very next one, it increases by 7. That is, the difference between one number and the next is 7. Therefore, we can add 7 to 36 and the result will be 43. Thus .

What does nextnumber do?

NextNumber finds the next number in a sequence of numbers Find next number About NextNumber• Classic Sequences• Contact NextNumber