Suppose that the sequence x, x1, x2... is defined by xo-1, x₁ =6, and xk+2=7xk+1-12x for 20. Find a general formula for xk. Be sure to include parentheses where necessary, e.g. to distinguish 1/(2k) from 1/2k. xk = 0

Q: For the sequence 1, 4, 7, 10, .. . its nth term is

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Q: Find a formula for 1/2+1/4+1/8+.+ 1/2h by examining the values of this expression for small values…

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Q: Show that An, n > 5 is simple.

A: Sol:- To show that An, the alternating group of even permutations of degree n, is simple for n ≥ 5,…

Q: ∞ Σ(n − 1)cn-1x² = − 1 − x + co +€₁x + Σcnx". n=2 n=2 Because the left-hand side contains neither a…

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Q: Find the sum of the first 15 terms of the arithmeticsequence with first term -4 and common…

A: Consider the given information as a=-4 and d=2

Q: Find the sum of n terms of an AP whose nth term is given by an=5-6n

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Q: Express the sum 3 + 5 + 7+ ... + (2k-1) using E-notation.

A: The given sum is 3+5+7+…+2k-1. Express the sum 3+5+7+…+2k-1 using ∑ notation as follows.

Q: Identify the closed form for the sequence: 1,0, 3, 2, 5, 4, 7, 6, .... (Note: The answer should not…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find the sum of first 24 terms of the list of numbers whose nth term is a, = 3 + 2n

A: Introduction :

Q: For the sequence an = an-1+ an-2 and a1 = 2, a2 = 3, its first term is 2 its second term is 3 its…

A: Recurrence sequence

Q: Find the 7th and 11th term of the expansion (y − x)^14

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Q: Find the sum of1/1 · 3 +1/3 · 5 +1/5 · 7 +··· .

A: The given series is, 11.3+13.5+15.7+..... Consider the first term, 11.3=12×1-12×1+1 Consider the…

Q: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

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Q: Find the sum of all integers that are multiples of 3 from 4 to 100.

A: We have to find the sum of all integers that are multiples of 3 from 4 to 100 Then, If A denotes the…

Q: What is the 100th term of a sequence of number in which, for every positive integer x, the sum of…

A: In the given question, concept of summation series is used. Summation Series The total of the series…

Q: 6h term of a G.P. is 9375 and its 4th term is 375. ind its 9th term.

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Q: Use the method of finite differences to find a closed polynomial formula for the following sequence…

A: 1, 3, 21, 91, 273, 651, 1333, 2451, 4161, 6643,... find the first difference D1=2,18, 70, 182,…

Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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Q: Find the surface area of each pyramid to the nearest whole number. 5. 3. 12 m 10 m 8m 4m

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Q: For number 51, can you show why -1/2  and 1/2 diverge and are not included.?

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Q: What is the coefficient of the 3rd term from the beginning in the expansion of the expression ( 2x-…

A: Given: a2x-y6

Q: ss the following as a factorial: 6 x 5 x 4 x 3x 2 x

A: The factorial function tells us to multiply all whole numbers down to 1 from the selected number.

Q: Find the sum of first 24 terms of the list of numbers whose nth term is a = 3 + 2n

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Q: Find for the sum of the first 50 negative even integers.

A: Negative even integers :-    -2,-4,-6,-8, ....... This is AP series with a=-2, d=-2