sequences - The sequence u_1, u_2, u_3, ... , is defined by the recurrence relation u_{n+1} = (-1)^n u_n + d, u_1 =2, where d is a constant.

Krishna (last edited 5 years ago) (Expert, Educator @Qalaxia)

Step 1: Find the required terms from the given rule.

[NOTE: Substitute the suitable n(position of the term(1sr,2nd,3d..)) value in the given rule to find the term]

EXAMPLE: To find the a_3 term, replace n with the 2

a_{n+1} = 4a_n - 7

a_{2+1} = 4a_2 - 7a 2+1 (since a_2=4k-7a

a_3 = 4(4k - 7) - 7

Step 2: Equate the term with the given value or substitute the terms in the given condition.

EXAMPLE: 4(4k-7) = 13

16k − 35 = 13

Step 3: Simplify the equation for the k(any variable) value