Subject: Mathematics
Book: Maths Mastery
Arithmetic series Sₙ= (n/2)(a₁+aₙ) or (n/2)[2a₁+(n–1)d] sums n terms. Geometric series Sₙ= a₁(1–rⁿ)/(1–r) for r≠1. These standard results handle repeated adding or multiplying patterns. For example, if an arithmetic sequence is 5, 8, 11,... with n=6 terms, sum is (6/2)[2×5+(6–1)×3]=3[10+15]=75. Mastery helps with finances (loan amortization), repeated additions in budgeting, or analyzing growth in discrete steps. Summation formulas are cornerstones of advanced math, bridging simple patterns to deep combinatorial or calculus expansions.
What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?
View QuestionIf the perimeter of a square is 40 cm, what is the area of the square?
View QuestionIf the product of two numbers is 120 and their sum is 26, what are the numbers?
View QuestionWhat is the HCF of 72 and 120?
View QuestionIf the sum of three consecutive integers is 96, what are the integers?
View QuestionA man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?
View QuestionA sum triples in 20 years at simple interest. What is the rate of interest per annum?
View QuestionThe LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?
View QuestionIf 2a + b = 10 and a - b = 4, what is the value of a?
View QuestionIf a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?
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