Question

Знайти s30якщо а21=17,d=2​

Answer 1

a₂₁ = 17;  d = 2

Первый член прогрессии:

а₁ + 20d = a₂₁

a₁ + 20*2 = 17

a₁ + 40 = 17

a₁ = -23

Сумма 30 первых членов:

$\tt S_{30}=\cfrac{2a_1+d(n-1)}{2}\cdot n= \cfrac{2\cdot(-23)+2(30-1)}{2}\cdot 30=180$

Ответ: 180

Answer 2

To find the value of s30 in an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1) * d

where: a_n is the nth term, a_1 is the first term (a21 in this case), d is the common difference between consecutive terms, n is the term number we want to find (n = 30 in this case).

Given that a21 = 17 and d = 2, we can substitute these values into the formula and solve for a30:

a30 = a1 + (30 - 1) * d a30 = 17 + (30 - 1) * 2 a30 = 17 + 29 * 2 a30 = 17 + 58 a30 = 75

So, the value of s30 is 75.