Question

arithmetic sequence

Answer 1

whats ur question do i need to define the term?

Answer 2

the 4th and 7th term of an arithmetic sequence are -8 and 4, respectively. find the first term and an explicit rule for the nth term

Answer 3

Do you know general formula for 'n' th term of arithmetic series ?

Answer 4

The common difference is
\[d =\frac{ 4-(-8) }{ 7-4 }\]
\[d =\frac{ 12 }{ 3 }\]
d = 4

Now the 4th term is

f(4) = a + 3d

where a is the first term and d is the common difference. d = 4. Thus

f(4) = a + 3(4)

f(4) = a + 12

f(4) = -8

Thus

a + 12 = -8

a = -20

You could have also used the fact that

f(7) = a + 6d

where d = 4

f(7) = a + 6(4)

f(7) = a + 24

f(7) = 4

a + 24 = 4

a = -20

Now the nth term is given by f(n) = a + (n - 1)d. Thus if a = -20 and d = 4, then

f(n) = -20 + (n - 1)(4)

f(n) = -20 + 4n - 4

f(n) = 4n - 24

∴ the first term is -20 and the general term is f(n) = 4n - 24.