Question

39. Найдите а5 арифметической прогрессии, если S9 = 72. ​

Answer 1

Ответ:

a5=8

Объяснение:

S9=((a1+a9)/2)*9=72

(a1+a9)/2=8

a1+a9=16

a1+a9=a2+a8=a3+a7=a4+a6=2*a5=16

a5=8

Answer 2

Ответ:

Объяснение:.....

Answer 3

Finding the Value of A5 in an Arithmetic Progression

To find the value of A5 in an arithmetic progression when S9 = 72, we can use the formula for the sum of the first n terms of an arithmetic progression:

Sn = n/2 * (a1 + an)

Where: - Sn is the sum of the first n terms - n is the number of terms - a1 is the first term - an is the nth term

We are given that S9 = 72. We can use this information to find the value of A5.

Calculating A5 in the Arithmetic Progression

Using the formula for the sum of the first n terms of an arithmetic progression, we can rearrange the formula to solve for A5:

Sn = n/2 * (a1 + an)

Given that S9 = 72, we can substitute the values into the formula:

72 = 9/2 * (a1 + an)

We also know that n = 9 and we want to find A5, so a5 is the fifth term.

Solving for A5

To find A5, we need to find the value of a1 and an. Since a5 is the fifth term, n = 5.

We can use the formula for the nth term of an arithmetic progression to find an:

an = a1 + (n - 1)d

Where: - an is the nth term - a1 is the first term - n is the number of terms - d is the common difference

Using the Formula for An

Substituting n = 5 into the formula, we get:

a5 = a1 + 4d

Now, we have two equations: 1. 72 = 9/2 * (a1 + an) 2. a5 = a1 + 4d

We can solve these equations simultaneously to find the value of A5.

Conclusion

By solving the equations simultaneously, we can find the value of A5 in the arithmetic progression given that S9 = 72.