Question

Сумма первых n членов арифметической прогрессии вычисляется по формуле Sn=(a1+an)2⋅n. Пользуясь этой формулой, вычисли значение a1, если an=14, Sn=144, n=8.

Answer 1

Ответ:

22

Объяснение:

$S_n=\frac{a_1+a_n}{2}*n$

$a_1=\frac{2S_n}{n}-a_n$

$a_n=14;S_n=144;n=8$

$a_1=\frac{2*144}{8}-14=22$

Answer 2

To find the value of $a_1$ (the first term) in an arithmetic progression, we are given the following information:

$a_n = 14$ (the nth term is 14) $S_n = 144$ (the sum of the first $n$ terms is 144) $n = 8$ (the number of terms is 8)

The formula to calculate the sum of the first $n$ terms of an arithmetic progression is $S_n = \frac{n}{2}(a_1 + a_n)$.

We can plug in the given values into the formula and solve for $a_1$:

$144 = \frac{8}{2}(a_1 + 14)$

First, let's simplify the equation:

$144 = 4(a_1 + 14)$

Now, distribute the 4:

$144 = 4a_1 + 56$

Subtract 56 from both sides:

$144 - 56 = 4a_1$

$88 = 4a_1$

Finally, divide by 4 to find the value of $a_1$:

$a_1 = \frac{88}{4} = 22$

So, the first term of the arithmetic progression is $a_1 = 22$.