The value of the a_5 is -405 if the a_1 =5 and a_n=-3a_{n-1} which is a geometric sequence with common ratio -3.
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
[tex]\rm a_1 = 5\\\\\rm a_n = -3a_{n-1}[/tex]
Plug n = 2
[tex]\rm a_2 = -3a_{2-1}\\\\\rm a_2 =- 3a_{1}\\\\a_2 = -15[/tex](as, [tex]\rm a_1 = 5[/tex])
Plug n = 3 we get:
[tex]a_3 = -45[/tex]
Plug n = 4, we get:
[tex]\rm a_4 =- 135[/tex]
Now plug n = 5, we get:
[tex]\rm a_5 = -405[/tex]
Thus, the value of the a_5 is -405 if the a_1 =5 and a_n=-3a_{n-1} which is a geometric sequence with common ratio -3.
Learn more about the sequence here:
brainly.com/question/21961097
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