Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Given formula: [tex]\sf A_n= -4(2)^{n-1}[/tex]
simplify substitute the number of term by replacing n
Find first five terms:
[tex]\sf A_1= -4(2)^{1-1}[/tex] ⇒ [tex]\sf A_1= -4[/tex]
[tex]\sf A_2= -4(2)^{2-1}[/tex] ⇒ [tex]\sf A_2= -8[/tex]
[tex]\sf A_3= -4(2)^{3-1}[/tex] ⇒ [tex]\sf A_3= -16[/tex]
[tex]\sf A_4= -4(2)^{4-1}[/tex]⇒ [tex]\sf A_4= -32[/tex]
[tex]\sf A_5= -4(2)^{5-1}[/tex]⇒ [tex]\sf A_5= -64[/tex]
Tenth term:
[tex]\sf A_{10}= -4(2)^{10-1}[/tex] ⇒ [tex]\sf A_{10}= -2048[/tex]
Answer:
[tex]\sf a_1=-4\\a_2=-12\\a_3=-20\\a_4=-28\\a_5=-36\\a_{10}=-76[/tex]
Step-by-step explanation:
[tex]\textsf{Given sequence}: \sf a_n=-4(2n-1)[/tex]
This formula is for the nth term of the sequence.
Therefore, to find any term of the sequence, substitute the position of the term you wish to find as n.
For example, to find the 10th term, substitute n = 10 into the formula:
[tex]\begin{aligned}\sf a_{10} & =-4[2(10)-1)]\\ & = -4(20-1)\\ & = -4(19)\\ & = -76\end{aligned}[/tex]
To find the first 5 terms, substitute n = 1 through n = 5 into the formula:
[tex]\sf a_1=-4[2(1)-1]=-4(2-1)=-4(1)=-4[/tex]
[tex]\sf a_2=-4[2(2)-1]=-4(4-1)=-4(3)=-12[/tex]
[tex]\sf a_3=-4[2(3)-1]=-4(6-1)=-4(5)=-20[/tex]
[tex]\sf a_4=-4[2(4)-1]=-4(8-1)=-4(7)=-28[/tex]
[tex]\sf a_5=-4[2(5)-1]=-4(10-1)=-4(9)=-36[/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.