Question

INHIB Знадіть перший імн арифметичної прогресії якщо а3=16 , а8=15​

Answer 1

Ответ:

16.4

Пошаговое объяснение:

а8=а3+5d

15=16+5d

5d=-1

d=-1/5

d=-0.2

a3=a1+2d

16=a1+2*(-0.2)

a1=16+0.4

a1=16.4

Answer 2

Finding the First Term of an Arithmetic Progression (AP)

To find the first term of an arithmetic progression (AP) when given two terms, we can use the formula:

a_n = a_1 + (n - 1)d

Where: - a_n is the nth term - a_1 is the first term - n is the term number - d is the common difference

Given Information

We are given: - a_3 = 16 - a_8 = 15

Using the Given Information to Find the First Term

We can use the formula to find the first term of the arithmetic progression.

For a_3 = 16: 16 = a_1 + 2d

For a_8 = 15: 15 = a_1 + 7d

Solving for the First Term

We can solve these two equations simultaneously to find the value of the first term, a_1.

Subtracting the first equation from the second equation: 15 - 16 = a_1 + 7d - (a_1 + 2d) -1 = 5d

So, d = -1/5.

Substituting the value of d into the first equation: 16 = a_1 + 2(-1/5) 16 = a_1 - 2/5 a_1 = 16 + 2/5 a_1 = 16 2/5 a_1 = 82/5 a_1 = 16.4

Conclusion

The first term of the arithmetic progression is 16.4.