find the 7th terms of the series 1/3+8/23+4/11.....

Question

Create a math-inspired image illustrating the concept of a sequential series. The image should feature a series of geometric shapes in ascending order to convey the idea of progression. Include a variety of different sized shapes to represent the diverse terms of the series. The image should also depict a noticeable emphasis or highlight on the 7th shape in the series. Make sure the image contains no text and is visually appealing.

find the 7th terms of the series 1/3+8/23+4/11.....

Answer 1

If 1/3+8/23+4/11..... is a harmonic series, then the corresponding arithmetic series is

3 + 23/8 + 11/4 + ...
= 24/8 + 23/8 + 22/8

so a = 3 and d = -1/8
term(7) = a + 6d
= 3 -6/8 = 9/4

so the 7th term of the HS is 4/9

Answer 2

i don't understand please help me any other examples

Answer 3

Insert 4H.M.s between 1and1/11

Answer 4

Well, let's see if we can find the pattern here.

Looking at the series, it seems like the numerator is doubling each time. So for the 7th term, we would have a numerator of 1 × 2^6 = 64.

Now, for the denominator, it seems to be increasing by 2 each time. So for the 7th term, the denominator would be 11 + (2 × 6) = 23.

So the 7th term of the series is 64/23. Just like that, a fraction that seems a bit out of whack. It's like ordering a single slice of pizza on a Friday night – it might leave you wanting more!

Answer 5

To find the 7th term of the series 1/3 + 8/23 + 4/11 ..., we need to first recognize the pattern in the series. From the given terms, we can observe that the denominator of each term is changing by multiplying it with consecutive even numbers, while the numerator appears to be decreasing by half in each term.

Let's break down the given terms:
1/3, 8/23, 4/11

The denominator changes as follows:
3, 23, 11

If we observe closely, we can recognize that the sequence of denominators can be represented as 3 * 2, 23 * 2, 11 * 2.

So, we can conclude that the 7th denominator will be 3 * 2^6, where 2^6 means 2 raised to the power of 6 (since we want the 7th term). Simplifying this expression, we have:

Denominator of the 7th term = 3 * 2^6 = 3 * 64 = 192

Now, let's consider the numerator. We can see a pattern of halving the numerator from term to term:

1, 8, 4

Based on this pattern, we can deduce that the 7th numerator will be 1/(2^(7-1)), where 7 is the term number we want. Simplifying this expression, we have:

Numerator of the 7th term = 1 / (2^6) = 1 / 64

Therefore, the 7th term of the series is 1/64 divided by 192.

7th term = (1/64) / 192
= 1 / (64 * 192)

Simplifying this further, we get:

7th term = 1 / 12288

Hence, the 7th term of the series 1/3 + 8/23 + 4/11 + ... is 1/12288.