Question

The fifth term of an arithmetic sequence is 23 and 12th term is 72

Answer 1

[AI-generated answer — Bot]

. What is the common difference?

The common difference is 8.

Answer 2

a+4d =23

a+11d=72
subtract
7d = 49
d = 49/7

the bot was wrong

Answer 3

again :(

Answer 4

[AI-generated answer — Explain Bot]

To find the common difference of an arithmetic sequence, we need two terms. In this case, we have the fifth term (a₅ = 23) and the twelfth term (a₁₂ = 72).

The formula for the nth term of an arithmetic sequence is given by:

aₙ = a₁ + (n-1)d

where:
aₙ is the nth term,
a₁ is the first term,
n is the position of the term,
d is the common difference.

To find the common difference (d), we can use the given information.

Step 1: Substitute the values into the formula for both the fifth term and the twelfth term:

a₅ = a₁ + (5-1)d
23 = a₁ + 4d

a₁₂ = a₁ + (12-1)d
72 = a₁ + 11d

Step 2: Solve the system of equations formed by the two equations.

From equation (1), we can rearrange it to get:
a₁ = 23 - 4d (equation 3)

Substitute equation (3) into equation (2):

72 = (23 - 4d) + 11d

Simplifying the equation:

72 = 23 + 7d

49 = 7d

d = 49/7 = 7

Therefore, the common difference (d) of the arithmetic sequence is 7.

To find the first term (a₁), substitute the value of d into equation (3):

a₁ = 23 - 4(7)
a₁ = 23 - 28
a₁ = -5

So, the first term (a₁) of the sequence is -5, and the common difference (d) is 7.