document.write( "Question 1173686: If 𝑓(1) = 3 and 𝑓(𝑛) = −2𝑓(𝑛 − 1) + 1,
\n" ); document.write( "then 𝑓(5) =
\n" ); document.write( "A. -5
\n" ); document.write( "B. 11
\n" ); document.write( "C. 21
\n" ); document.write( "D. 43 \n" ); document.write( "
Algebra.Com's Answer #798960 by mila nedic(19)\"\" \"About 
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𝑓(𝑛) = −2𝑓(𝑛 − 1) + 1
\n" ); document.write( "𝑓(5) =
\n" ); document.write( "All we have to do here is to replace each n with 5 and continue until we get to 𝑓(1) which we know is 3.
\n" ); document.write( "𝑓(5) = −2𝑓(5 − 1) + 1
\n" ); document.write( " =-2𝑓(4)+1 (now we need to figure out 𝑓(4)
\n" ); document.write( "𝑓(4)=−2𝑓(4 − 1) + 1
\n" ); document.write( " =-2𝑓(3)+1 (now we need 𝑓(3)
\n" ); document.write( "𝑓(3)=−2𝑓(3 − 1) + 1
\n" ); document.write( " =-2𝑓(2)+1 (now we need 𝑓(2)
\n" ); document.write( "𝑓(2)=−2𝑓(2 − 1) + 1
\n" ); document.write( " =-2𝑓(1)+1
\n" ); document.write( " =-2(3)+1 (we can replace 𝑓(1) with 3 because we know they are equal)
\n" ); document.write( " =-5 (𝑓(2) is -5 so now we go back up until we get to 𝑓(5))\r
\n" ); document.write( "\n" ); document.write( "𝑓(3)=−2𝑓(3 − 1) + 1
\n" ); document.write( " =-2𝑓(2)+1
\n" ); document.write( " =-2(-5)+1 (we can replace 𝑓(2) with -5 since we solved that in the last step)
\n" ); document.write( " =11
\n" ); document.write( "𝑓(4)=−2𝑓(4 − 1) + 1
\n" ); document.write( " =-2𝑓(3)+1
\n" ); document.write( " =-2(11)+1 (we can replace 𝑓(3) with 11)
\n" ); document.write( " =-21
\n" ); document.write( "𝑓(5) = −2𝑓(5 − 1) + 1
\n" ); document.write( " =-2𝑓(4)+1
\n" ); document.write( " =-2(-21)+1 (we can replace 𝑓(4) with -21)
\n" ); document.write( " =43 (𝑓(5) is 43)\r
\n" ); document.write( "\n" ); document.write( "Therefore 𝑓(5) is equal to D. 43.
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