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The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it?
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The number of the terms of the series 10 9 2/3 9 1/3 9 .will amo...
Solution:

To find out the number of terms in the series, we need to first find out the common difference between the terms.

Step 1: Finding the common difference
We can see that the common difference between the terms is -10/3.

Step 2: Finding the nth term of the series
The nth term of the series can be calculated using the formula:

an = a1 + (n-1)d

where
an = nth term
a1 = first term
d = common difference

Substituting the values in the formula, we get:

an = 10 + (n-1) (-10/3)
an = 10 - (10/3)(n-1)
an = (30 - 10n + 10)/3
an = (40 - 10n)/3

Step 3: Finding the value of n
We want the sum of the series to be equal to 155. The sum of the series can be calculated using the formula:

Sn = n/2 (a1 + an)

Substituting the values, we get:

155 = n/2 (10 + (40 - 10n)/3)
310 = n(30 - 3n + 10)
310 = n(40 - 3n)
310 = 40n - 3n^2
3n^2 - 40n + 310 = 0

Solving the quadratic equation, we get:

n = 20 or n = 51.67

Since n has to be a whole number, we take n = 20.

Therefore, the number of terms in the series is 20.
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The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it?
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