Question

A11=6 a20=12 a1=? d=?

Answer 1

A11=a1+10d=6
a20=a1+19d==12

a1+19d=a1+10d+9d=12

6+9d=12
9d=6
d=6:9
d=2/3
a1+19*2/3=12
a1+12 2/3=12
a1=12-12 2/3
a1=-2/3

Answer 2

A11=a1+10d
a20= a1+19d

a1+10d=6
a1+19d=12

6-10d=12-19d
-10d+19d=12-6
9d=6
d=2/3
a1=6-10d= 6-20/3= 18/3-20/3= -2/3
Ответ: a1= -2/3; d= 2/3

Answer 3

To find the values of a1 and d in the arithmetic sequence, we'll first need to understand the pattern.

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. The common difference (d) between consecutive terms is the same throughout the sequence.

Given: A11 = 6 (eleventh term of the sequence is 6) A20 = 12 (twentieth term of the sequence is 12)

To find a1 (the first term) and d (the common difference), we can use the formulas for arithmetic sequences:

1. Formula for the nth term of an arithmetic sequence: An = a1 + (n - 1) * d

2. Formula for the arithmetic mean of two terms in an arithmetic sequence: (Am) = (An1 + An2) / 2

Using the information given:

For n = 11: A11 = a1 + (11 - 1) * d 6 = a1 + 10d ...........(1)

For n = 20: A20 = a1 + (20 - 1) * d 12 = a1 + 19d ...........(2)

Now, we have a system of two equations with two unknowns (a1 and d). We can solve these equations to find the values of a1 and d.

Step 1: Solve Equation (1) for a1: a1 = 6 - 10d

Step 2: Substitute the value of a1 from Step 1 into Equation (2): 12 = (6 - 10d) + 19d

Step 3: Simplify the equation and solve for d: 12 = 6 + 9d

Step 4: Solve for d: 9d = 12 - 6 9d = 6 d = 6 / 9 d = 2/3

Now that we have found the common difference (d), we can find the first term (a1) by substituting the value of d into Equation (1):

a1 = 6 - 10 * (2/3) a1 = 6 - (20/3) a1 = 18/3 - 20/3 a1 = -2/3

So, the first term (a1) is -2/3, and the common difference (d) is 2/3.