Sequences and Series

Formula for recurrence relation

t_n = r x t_n-1 + d

Where tn is the nth term, r is the common ratio, and d is the constant difference.

Formula of Arithmetic Sequences

t_{n = a + (n-1)d, where a is the first term and d is the common difference.}

t_n = t_n-1 +d, where d is the common difference

Formula for recurrence relation

t_n = r x t_n-1 + d

Where tn is the nth term, r is the common ratio, and d is the constant difference.

Formula of Arithmetic Sequences

t_{n = a + (n-1)d, where a is the first term and d is the common difference.}

t_n = t_n-1 +d, where d is the common difference

Formula of Arithmetic Series

S_n = n/2( 2a + d(n-1)), where Sn is the sum of the first n terms, a is the first term, and d is the common difference.

S_{n = n/2( a + l), where l is tn}

Formula of Geometric sequences

tn = a x r^n-1, where a is the first term and r is the common ratio.

t_n = r x t_n-1 , where r is the common ratio

Formula for Geometric Series

S_n = a(rⁿ-1) / r-1