Question

Help ASAP.

Find the first, fourth, and eighth terms in the sequence. (A( n )=-2*5^n-1
a) -2; - 250; -156,250
b) -10; -1,000; -10,000,000
c) 0; -250; -156,250
d) -10; -1,250; -781,250
Write a rule for a geometric sequence that has negative 6 as its first term and a common ratio of 2. What is the tenth term of this sequence?

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(1)/(2)=-3\cdot2^n\\\\\boxed{Answer:\ A(n)=a_n=-3\cdot2^n}`