Question

A1=56 d=-3 n=11 найти an и Sn

Answer 1

$a_1=56\\d=-3\\n=11\\a_n-?\\S_n-?\\\\a_n=a_{11}=a_1+10d=56+10(-3)=56-30=26\\S_n=S_{11}=(a_1+a_{11})*11:2=(56+26)*11:2=82*11:2=451$

Answer 2

To find the value of the nth term (an) and the sum of the first n terms (Sn) of an arithmetic sequence, you can use the following formulas:

an = A1 + (n - 1) * d Sn = (n/2) * (2 * A1 + (n - 1) * d)

Given the following values: A1 = 56 (the first term of the arithmetic sequence) d = -3 (the common difference between consecutive terms) n = 11 (the number of terms)

Let's substitute these values into the formulas to find the values of an and Sn.

Calculating the nth term (an): an = A1 + (n - 1) * d an = 56 + (11 - 1) * (-3) an = 56 + 10 * (-3) an = 56 - 30 an = 26

Therefore, the value of the 11th term (an) is 26.

Calculating the sum of the first n terms (Sn): Sn = (n/2) * (2 * A1 + (n - 1) * d) Sn = (11/2) * (2 * 56 + (11 - 1) * (-3)) Sn = (11/2) * (2 * 56 + 10 * (-3)) Sn = (11/2) * (112 + (-30)) Sn = (11/2) * 82 Sn = 451

Therefore, the sum of the first 11 terms (Sn) is 451.