Find the next five terms of each of the following sequences given by :
$ a_{1}=a_{2}=2, a_{n}=a_{n-1}-3, n>2 $

Given:

\( a_{1}=a_{2}=2, a_{n}=a_{n-1}-3, n>2 \)
To do:

We have to find the next five terms of the given sequence.
Solution: 

The next five terms in the sequence are obtained by substituting $n=3, 4, 5, 6, 7$ respectively.

When $n=3$,

$a_3=a_{3-1}-3$

$=a_2-3$

$=2-3$

$=-1$

When $n=4$,

$a_4=a_{4-1}-3$

$=a_3-3$

$=-1-3$

$=-4$

When $n=5$,

$a_5=a_{5-1}-3$

$=a_4-3$

$=-4-3$

$=-7$

When $n=6$,

$a_6=a_{6-1}-3$

$=a_5-3$

$=-7-3$

$=-10$

When $n=7$,

$a_7=a_{7-1}-3$

$=a_6-3$

$=-10-3$

$=-13$

Therefore, the next five terms of the given sequence are $-1, -4, -7, -10$ and $-13$. 

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Updated on: 10-Oct-2022

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