Question

Первый член арифметической прогрессии равен 2,а разность равна 3. найти седьмой член прогрессии. помогите решить

Answer 1

$a _{n} = a _{1} + d (n-1)$

а1 = 2
d =3
n =7

a7 = 2 +3 (7 - 1) = 2 + 3 * 6 = 2+18 = 20

Answer 2

$a _{1} =2 \\ d=3 \\ \\ a _{7} =a _{1} +6d=2+3*6=2+18=20$

Answer 3

Arithmetic Progression Calculation

To find the seventh term of an arithmetic progression with the first term \(a_1 = 2\) and the common difference \(d = 3\), we can use the formula for the \(n\)th term of an arithmetic progression:

\[a_n = a_1 + (n-1)d\]

Substitute the given values:

\[a_7 = 2 + (7-1) \times 3\]

\[a_7 = 2 + 6 \times 3\]

\[a_7 = 2 + 18\]

The seventh term of the arithmetic progression is 20.

Explanation

The formula for the \(n\)th term of an arithmetic progression is \(a_n = a_1 + (n-1)d\), where \(a_n\) is the \(n\)th term, \(a_1\) is the first term, \(n\) is the term number, and \(d\) is the common difference.

Using the given values of \(a_1 = 2\) and \(d = 3\), we substitute these into the formula to find the seventh term \(a_7 = 2 + (7-1) \times 3 = 20\)