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# SAT Sequences and Series

$$1, -8, t, -62, -134, \ldots$$

In the sequence above, the first term is $$1$$. Each term after the first is $$10$$ less than $$2$$ times the previous term. What is the value of $$t$$?

(A) $$\ \ -278$$
(B) $$\ \ -26$$
(C) $$\ \ -18$$
(D) $$\ \ 8$$
(E) $$\ \ 10$$

$$M=12341234\ldots 1234$$

$$M$$ is formed by writing $$1234$$ repeatedly, as shown above. If $$M$$ has $$128$$ digits, which of the following is the sum of its digits?

(A) $$\ \ 10$$
(B) $$\ \ 32$$
(C) $$\ \ 128$$
(D) $$\ \ 320$$
(E) $$\ \ 3200$$

In the decimal $$0.9756497564\ldots$$, the digits $$97564$$ repeat indefinitely. Which digit is in the $$4192$$th place to the right of the decimal point?

(A) $$\ \ 9$$
(B) $$\ \ 7$$
(C) $$\ \ 6$$
(D) $$\ \ 5$$
(E) $$\ \ 4$$

Consider the arithmetic sequence $$1, \frac{1}{2}, 0, -\frac{1}{2}, \ldots$$. What is the $$8$$th term in the sequence?

(A) $$\ \ -3$$
(B) $$\ -\frac{5}{2}$$
(C) $$\ \ -2$$
(D) $$\ \ \frac{5}{2}$$
(E) $$\ \ 8$$

$$28, 7, \frac{7}{4}, \frac{7}{16}, \ldots$$

In the sequence above, each term is obtained by multiplying the preceding term by $$\frac{1}{4}$$. What is the $$91$$th term of the sequence?

(A) $$\ \ (\frac{1}{4})^{89}$$
(B) $$\ \ 7 (\frac{1}{4})^{89}$$
(C) $$\ \ 28 (\frac{1}{4})^{89}$$
(D) $$\ \ 7(\frac{1}{4})^{90}$$
(E) $$\ \ 7(\frac{1}{4})^{91}$$

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