![]() Learn more about our Matrix+ Online Maths Adv Course now. Learn from expert Maths teachers at the comfort of your own home! You will have access to theory video lessons, receive our comprehensive workbooks sent to your front door, and get help through Q&A discussion forums with Matrix+ Online Courses. Arithmetic and Geometric Series Definitions: First term: a 1 Nth term: a n Number of terms in the series: n Sum of the first n terms: S n Difference between successive terms: d Common ratio: q Sum to infinity: S Arithmetic Series Formulas: a a n dn + 1 (1) 1 1 2 i i i a a a + + 1 2 n n a a S n + 2 11 ( ) n 2. Recognise and use the recursive definition of an arithmetic sequence: \( T_ \) as the simplest rational number.When you know the first term and the common difference. Know the difference between a sequence and a series Series (Find the sum) When you know the first and last term. ![]() Integral Test Ifanf(n) whenf(x) is a positive, continuous, eventuallydecreasing function, then Z1 anconverges ()f(x)dxconverges n11 ComparisonTest Supposeanandbnare two positive sequences, withan bnfor alln > Nfor some numberN. A sequence is the set of ordered elements that follow. Divergence Test If liman6 0, then the series Panis divergent. Sequence and series formulas are related to different types of sequences and series in math. NESA requires students to be proficient in the following syllabus outcomes: 1converges whenp np 1, otherwise diverges.
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