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Sequences and series are employed in both mathematics and everyday life. The Sequence is a collection of numbers arranged in a specific order or according to a range of criteria. The digits of a sequence are summed together to form a series.
In Sequence, items are arranged in a specific order according to principles. In Sequence, a distinct pattern of numbers is crucial. In Sequence, the order in which the numbers appear is crucial.
The elements do not have to be in any particular order in a series. In a series, the number pattern is unimportant. In a series, the Sequence of appearance is also unimportant.
Formulas related to Sequence and Series: There are a variety of formulas for various patterns and Series. We can use them to identify a combination of unknown parameters such as the first term, the nth term, common variables, and so on. Each type of Sequence and Series does have its own set of formulae. The following are formulas for several sequences and Series.
Formulas for Arithmetic Sequences and Series
The following are the many formulas used in an arithmetic sequence:
To find the Arithmetic sequence | x, x + d, x + 2d, x + 3d, … |
To find the Arithmetic series | x + (x + d) + (x + 2d) + (xa + 3d) + … |
First term: | x |
To find the Common difference(d): | A term which is successive – Term which is Preceding or xn−xn−1xn−xn−1 |
To find the nth term xn | x + (n-1)d |
To find the Sum of the arithmetic series Sn | (n/2)(2x + (n-1)d) |
Formulas for Geometric Sequences and Series
The following are the various formulas used in geometric Sequence:
To find the Geometric sequence | x, xr, xr2,….,xr(n-1),… |
To find the Geometric series | x + xr + xr2 + …+ xr(n-1)+ … |
To find the First term | x |
To find the Common ratio | r |
To fnd the nth term | xr(n-1) |
To find the Sum of geometric series | Finite series: Sn = x(1−rn)/(1−r) for r≠1, and Sn = xn for r = 1 Infinite series: Sn = x/(1−r) for |r| < 1, and not defined for |r| > 1 |
Picture series and sequences:
Sequence and series pictures from reasoning problems based on a succession of images, such as a query with five figures in a row, labelled A, B, C, D, and E. These are classified as problem figures because they show a progression of change. Following the problem, figures are five answer figures: 1,2,3,4 and 5. You must select one answer figure from a group of five to continue the Sequence started by the problem figures.
Problems based on Picture Series and Sequences:
Example:
A series of pictures will be given in this type of question. Few questions will have the first and last figures being identical. The requirement is to choose the figure that will continue the Series from the given options.
We may infer from the above diagram that because the first and last pictures are the same, the next picture would be the same as the second image in the given details. As a result, the solution figure is identical to the second figure.
Question: Which of the following response figures will continue the Series started by the problem figures?
The answer is Option 3. The shaded area advances one step clockwise. In addition, after one step, an extra part is shaded. As a result, the Series will continue with the answer in figure 3.
Conclusion
We discussed a Series of pictures and Sequences, Formulas related to Sequence and Series, sequence and series pictures, and other related topics through the study material notes on Picture Series and Sequences. We also discussed Sequence and Series Formula related to Arithmetic & Formulas for Geometric Sequences and Series to give you proper knowledge.
There are enjoyable problems in which the next number in the Series must be found. In such challenges, a numerical series is supplied. This numerical Sequence follows a specific pattern. This pattern must be discovered, and the next step in the Series must be calculated. Number puzzles are comparable to pattern image or picture puzzles.
Instead of numbers, visuals are employed here. A certain picture will be seen, and the solution will be found that follows a specific pattern. The pattern must be visually interpreted in order to predict what will happen next in the pattern. Non-Verbal Ability is the Ability to interpret visual information.
