Question

Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form. a1 = – 25 an = an–1–14 an=

Answer 1

Given :

$a_1=-25$ .

$a_n=a_{n-1}-14$ .

To Find :

The general equation of $a_n$ .

Solution :

We know , when difference between any two consecutive terms in an A.P is equal , then the series is in arithmetic progression .

Now , common difference ,

$d=a_n-a_{n-1}\\\\d=-14$

Also , first term is -25 .

Now , general term of an A.P is given by :

$a_n=a+(n-1)d\\\\a_n=-25+(n-1)(-14)\\\\a_n=-25-14n+14\\\\a_n= -11-14n$

Hence , this is the required solution .