The sum of the first eight terms of the geometric sequence whose first term is -2.5 and ratio is 2 is: -637.5
The nth term of a geometric sequence is given mathematically as;
T(n) = ar^n
- where, a = first term of the geometric sequence.
- r = common ratio of the sequence
- and n = nth term of the sequence.
Therefore, the sum of the first 8 terms of the geometric sequence is;
- <em>S(8) = a + ar + ar² + ar³ + ar⁴ + ar⁵ + ar⁶ + ar⁷.</em>
In essence;
- since common ratio, r = 2
Therefore, we have;
- S(8) = -2.5(1 + 2 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷)
S(8) = -637.5.
Therefore, the sum of the first eight terms of the <em>geometric sequence</em> whose first term is -2.5 and ratio is 2 is: -637.5
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Answer:
Fredholm's integral equations of the first kind are the prototypical example of ill-posed linear inverse problems. The model, among other things, reconstruction of distorted noisy observations and indirect density estimation and also appear in instrumental variable regression. However, their numerical solution remains a challenging problem. Many techniques currently available require a preliminary discretization of the domain of the solution and make strong assumptions about its regularity. For example, the popular expectation-maximization smoothing (EMS) scheme requires the assumption of piecewise constant solutions which is inappropriate for most applications. We propose here a novel particle method that circumvents these two issues. This algorithm can be thought of as a Monte Carlo approximation of the EMS scheme which not only performs an adaptive stochastic discretization of the domain but also results in smooth approximate solutions. We analyze the theoretical properties of the EMS iteration and of the corresponding particle algorithm. Compared to standard EMS, we show experimentally that our novel particle method provides state-of-the-art performance for realistic systems, including motion deblurring and reconstruction of cross-section images of the brain from positron emission tomography.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Because when you multiply 23.67 by 28 then you add then you get your answer.
Since the roots are 2,3i, and -3i, you can write it as
(x-2)(x-3i)(x+3i)=(x-2)(x^2+9)=x^3-2x^2+9x-18.
