Question

http://prntscr.com/amimft @imqwerty

Answer 1

here the x coordinate of the points represent "n"
and the y coordinates represent "\(a_n\)"

we will solve this question by trying out the options
by "trying out the options" i meant that we will select any of the 3 given points and substitute the value of n ( the x coordinate) into the options
the option which gives the correct value of corresponding \(a_n\) to that "n" is correct

it may happen that 2 options give correct value of "\(a_n\)" for a particular "n"
in that case try another "n" ( i mean another point :) )

Answer 2

Uhh ok tell me how to start it lol im slow on this one

Answer 3

okay
well the point (1,3) looks cute so we will start off with it

so the correct option will give "\(a_n=3\)" when we put "\(n=1\)" in it

\(\color{blue}{option~1}\)
\(a_n=3 \large \left(\frac{1}{5}\right)^{n-1}\)
putting n=1

\(a_n=3 \large \left(\frac{1}{5}\right)^{1-1}\)
\(a_n=3 \large \left(1\right)\)
\(a_n=3\)

\(\color{blue}{option~2}\)
\(a_n=3(-5)^{n-1}\)
\(a_n=3(-5)^{1-1}\)
\(a_n=3(1)\)
\(a_n=3\)

\(\color{blue}{option~3}\)
\(a_n=0.3(5)^{n-1}\)
\(a_n=0.3(5)^{1-1}\)
\(a_n=0.3(1)\)
\(a_n=0.3\)

similarly you can try out the 4th option

now here we see that options 1 and 2 are giving correct value for \(a_n\) so they might be correct
but option 3 is giving wrong value of \(a_n\) so it is wrong

now we need to find which one of options1 or 2 is correct
so wee will take another point (for example (2,0.6)) and then check

Answer 4

How did you get the 3(1) each time for the first 2? Like where did the -5 go?

Answer 5

anything raised to the power "0" is "1" \(\color{red}{except~this~case- 0^0}\)

so like in 1st equation we had this-
\(a_n=3 \large \left(\frac{1}{5}\right)^{1-1}\)
\(a_n=3 \large \left(\frac{1}{5}\right)^{0}\)
\(a_n=3 \large \left(1\right)\)

Answer 6

Yeaa uh I can't process this one so ima guess the second option is right xD

Answer 7

noo thats wrong cx

Answer 8

1st option

Answer 9

e.e thats correct

Answer 10

xD

Answer 11

:)