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lapo4ka [179]
2 years ago
12

Evaluate.

Mathematics
1 answer:
const2013 [10]2 years ago
6 0

9514 1404 393

Answer:

  -1/6

Step-by-step explanation:

A suitable calculator can evaluate this for you and show you the result as a fraction.

You start with the multiplication in the inner-most set of brackets. Here, those brackets are the absolute value function.

  -2(-1/3) = +2/3

Then the sum in those brackets:

  -5/6 +2/3 = -5/6 +4/6 = -1/6

The absolute value changes the sign of this back to positive, so the value in square brackets is ...

  3 -(1/6) = 18/6 -1/6 = 17/6

Finally, this value is divided by -17, so you have ...

  \dfrac{17}{6}\div(-17)=\dfrac{17}{6}\cdot\dfrac{-1}{17}=-\dfrac{17\cdot1}{17\cdot6}=\boxed{-\dfrac{1}{6}}

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Given:

First term of an arithmetic sequence is 2.

Sum of first 15 terms = 292.5

To find:

The common difference.

Solution:

We have,

First term: a=2

Sum of first 15 terms: S_{15}=292.5

The formula of sum of first n terms of an AP is

S_n=\dfrac{n}{2}[2a+(n-1)d]

Where, a is first term and d is common difference.

Putting S_{15}=292.5, n=15 and a=2 in the above formula, we get

292.5=\dfrac{15}{2}[2(2)+(15-1)d]

292.5=\dfrac{15}{2}[4+14d]

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Divide both sides by 15.

\dfrac{292.5}{15}=2+7d

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19.5-2=7d

17.5=7d

Dividing both sides by 7, we get

\dfrac{17.5}{7}=d

2.5=d

Therefore, the common difference is 2.5.

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