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# Grade 12 Mathematics: Sequences and Series

Explore the fundamental concepts of arithmetic sequences, series summation, and patterns in Grade 12 mathematics with this quiz. This quiz is based on the Via Afrika Gr12 Mathematics Study Guide and includes exemplar exercises.

Created by
@PurposefulElectricOrgan

### What is the general formula for finding the nth term in an arithmetic sequence?

$T_n = a+(n-1)d$

### What is the general formula for finding the sum of the first n terms in an arithmetic sequence?

$S_n = n(2a+(n-1)d)$

### What defines a geometric sequence?

Each term is found by multiplying the preceding term by a fixed number.

### What is the formula for finding the nth term in a geometric sequence?

<p>$T_n = ar^{n-1}$</p> Signup and view all the answers

### What is the formula for finding the sum of the first n terms in a geometric sequence?

<p>$S_n = a(1-r^n)/(1-r)$</p> Signup and view all the answers

### Under what condition does an infinite geometric series exist?

<p>$|r| &lt; 1$</p> Signup and view all the answers

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