The type of progression of the given series and hence its sum.
Answer to Problem 12CT
The given series is an arithmetic progression. Sum of the series is 45.
Explanation of Solution
Given: The given series is-
Concept Used: The sum of any series can be represented using the summation sign as follows-
This represents a series whose
A series is said to be an Arithmetic Progression (or A.P) if the difference between any two consecutive terms, namely the
This constant d is called the common difference. Sum of n terms of any A.P having first term a and common difference d can be determined using the formula-
A series is said to be a Geometric Progression (or G.P) if the ratio of two consecutive terms, namely
This constant r is called the common ratio. Sum of n terms of any G.P having first term a and common ratio r can be determined using the formula-
Calculations: The given series is-
Thus, the
Thus,
Now,
Since the difference of two consecutive terms is a constant hence the given series is an A.P series with common difference
Thus, the sum of the series can be determined as follows-
Hence, the sum of the given series is 45.
Chapter 8 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning