Question

A3=1, d=2, an=51n-? Sn-?​

Answer 1

Ответ:     28.    672.

Объяснение:

Дано

a(n) - арифметическая прогрессия

a(3)=1;

d=2;

a(n)=51;

*******

n=?  S(n)=?

Решение

a(n) = a1+(n-1)*d.

a(3) = a1+(3-1)*2 => 1;

a(1) = 1-4 = -3.

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-3+(n-1)*2=51;

n-1=(51+3)/2

n-1=27;

n=27+1=28.

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S(28) = 28(a1+a28)/2.

a(28) =51;

S(28)=28(-3+51)/2 = 28*48/2 = 14*48 = 672.

Answer 2

It appears that you are dealing with an arithmetic sequence, where A3 represents the third term, d is the common difference, an represents the nth term, and Sn represents the sum of the first n terms.

In your sequence, A3 is given as 1, and d is given as 2. To find the nth term (an) and the sum of the first n terms (Sn), we can use the following formulas:

1. nth Term (an) of an Arithmetic Sequence: an = A1 + (n - 1)d

2. Sum of the First n Terms (Sn) of an Arithmetic Sequence: Sn = (n/2) * [2A1 + (n - 1)d]

Given A3 = 1 and d = 2, let's calculate an and Sn:

1. Calculate A1: A1 = A3 - 2d A1 = 1 - 2 * 2 A1 = 1 - 4 A1 = -3

Now that we have A1, we can use the formulas to find an and Sn for any value of n.

a. For an: an = -3 + (n - 1) * 2 an = -3 + 2n - 2 an = 2n - 5

b. For Sn: Sn = (n/2) * [2 * (-3) + (n - 1) * 2] Sn = (n/2) * [-6 + 2n - 2] Sn = (n/2) * [-8 + 2n]

Now you have the formulas for an and Sn in terms of n:

• an = 2n - 5
• Sn = (n/2) * [-8 + 2n]

You can use these formulas to find the nth term and the sum of the first n terms for any specific value of n in the arithmetic sequence.