Question

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Answer 1

$1.\\A(n)=-2\cdot5^{n-1}\\\\\text{Find the first, fourth, and eighth terms}\\\text{It means}\ A(1),\ A(4)\ \text{and}\ A(8).\\\\\text{Substitute}\ n=1,\ n=4\ \text{and}\ n=8\ \text{in}\ A(n):\\\\A(1)=-2\cdot5^{1-1}=-2\cdot5^0=-2\cdot1=-2\\\\A(4)=-2\cdot5^{4-1}=-2\cdot5^3=-2\cdot125=-250\\\\A(8)=-2\cdot5^{8-1}=-2\cdot5^7=-2\cdot78,125=-156,250\\\\\boxed{Answer:\ a)\ -2,\ -250,\ -156,250}.$

$2.\\a_1=-6,\ r=2\\\\\text{The formula of a n-th term of geometric sequence}\\\\a_n=a_1r^{n-1}\\\\\text{Substitute:}\\\\a_n=-6\cdot2^{n-1}=-6\cdot2^n\cdot2^{-1}=-6\cdot2^n\cdot\dfrac{1}{2}=-3\cdot2^n\\\\\boxed{Answer:\ A(n)=a_n=-3\cdot2^n}$