Question

Дана арифметическая прогрессия an вычислите сумму 8 членов,если a5=-3 d=-4

Answer 1

А5=а1+d(n-1);
-3=a1-4•4;
a1-16=-3;
a1=-3+16;
a1=13;
Sn=(2a1+d(n-1))/2•n;
S8=(26-4•7)/2•8=-2/2•8=-8;

Answer 2

Understanding the problem

We are given an arithmetic progression with the formula `an`, where `a` is the first term and `d` is the common difference. We need to find the sum of the first 8 terms of this arithmetic progression, given that the 5th term `a5` is equal to -3 and the common difference `d` is equal to -4.

Solving the problem

To find the sum of the first 8 terms, we can use the formula for the sum of an arithmetic progression:

Sum = (n/2) * (2a + (n-1)d)

Where: - `n` is the number of terms (in this case, 8) - `a` is the first term (unknown) - `d` is the common difference (known)

Let's solve for `a` using the information given.

Given: `a5 = -3` and `d = -4`

From the formula for the nth term of an arithmetic progression, we can write: a5 = a + (5-1)d

Substituting the given values, we have: -3 = a + 4*(-4)

Simplifying the equation, we get: -3 = a - 16

Adding 16 to both sides, we have: a = 13

Now that we have the value of `a`, we can calculate the sum of the first 8 terms.

Substituting the values into the formula, we have: Sum = (8/2) * (2*13 + (8-1)*(-4))

Simplifying the equation, we get: Sum = 4 * (26 + 7*(-4))

Simplifying further, we have: Sum = 4 * (26 - 28)

Sum = 4 * (-2)

Finally, calculating the sum, we have: Sum = -8

Therefore, the sum of the first 8 terms of the arithmetic progression is -8.