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NNADVOKAT [17]
3 years ago
12

in a AP the first term is 8,nth term is 33 and sum to first n terms is 123.Find n and common difference​

Mathematics
1 answer:
allsm [11]3 years ago
8 0

I believe there is no such AP...

Recursively, this sequence is supposed to be given by

\begin{cases}a_1=8\\a_k=a_{k-1}+d&\text{for }k>1\end{cases}

so that

a_k=a_{k-1}+d=a_{k-2}+2d=\cdots=a_1+(k-1)d

a_n=a_1+(n-1)d

33=8+(n-1)d

21=(n-1)d

n has to be an integer, which means there are 4 possible cases.

Case 1: n-1=1 and d=21. But

\displaystyle\sum_{k=1}^2(8+21(k-1))=37\neq123

Case 2: n-1=21 and d=1. But

\displaystyle\sum_{k=1}^{22}(8+1(k-1))=407\neq123

Case 3: n-1=3 and d=7. But

\displaystyle\sum_{k=1}^4(8+7(k-1))=74\neq123

Case 4: n-1=7 and d=3. But

\displaystyle\sum_{k=1}^8(8+3(k-1))=148\neq123

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Step-by-step explanation:

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3 years ago
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ss7ja [257]

Answer:

64

Step-by-step explanation:

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2³ means to multiply 2 by itself 3 times

so it would be

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hope this helps!

6 0
2 years ago
You stand 50 feet from a monument. The angle of depression from the top of the monument to your feet is 64 degrees. Approximatel
Murrr4er [49]

Answer:

The monument is approximately 86.6 feet tall

Step-by-step explanation:

The given monument parameters are;

The distance of the person from the monument = 50 feet

The angle of depression from the top of the monument to the person's feet = 64°

Given that the angle of elevation to the top of the monument from the person's feet = The angle of depression from the top of the monument to the person's feet, we have;

tan(Angle of depression) = tan(Angle of elevation) = (The height of the monument)/(The distance from the monument)

∴ The height of the monument = tan(Angle of depression) × The distance from the monument

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The height of the monument = tan(60°) × 50 ≈ 86.6

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7 0
3 years ago
A) Expand and simplify (4x + 3)(2x - 5)
Delicious77 [7]

Answer:

8x² - 14x - 15

Step-by-step explanation:

(4x + 3)(2x - 5)

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6 0
3 years ago
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zheka24 [161]

Answer:

a=7.85-1/2^b

Step-by-step explanation:

2a=15.7-b Move variable to the right side and change its sign

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