The nth term of an arithmetic progression is given by an =3n-2,then the 12term is
Answers
Step-by-step explanation:
n=12
an=3×12-2
an=36-2
an=34
EXPLANATION.
Nth term of an A.P.
⇒ Aₙ = 3n - 2.
As we know that,
Put the value of n = 1 in the equation, we get.
⇒ 3(1) - 2.
⇒ 3 - 2 = 1.
Put the value of n = 2 in the equation, we get.
⇒ 3(2) - 2.
⇒ 6 - 2 = 4.
Put the value of n = 3 in the equation, we get.
⇒ 3(3) - 2.
⇒ 9 - 2 = 7.
Put the value of n = 4 in the equation, we get.
⇒ 3(4) - 2.
⇒ 12 - 2 = 10.
Series = 1, 4, 7, 10, . . . . .
First term = a = 1.
Common difference = d = b - a = c - b.
Common difference = d = 4 - 1 = 3.
As we know that,
General term of an A.P.
⇒ Tₙ = a + (n - 1)d.
To find 12th term of an A.P.
⇒ T₁₂ = a + (12 - 1)d.
⇒ T₁₂ = a + 11d.
Put the values in the equation, we get.
⇒ T₁₂ = 1 + 11(3).
⇒ T₁₂ = 1 + 33.
⇒ T₁₂ = 34.
MORE INFORMATION.
Supposition of terms in an A.P.
(1) = Three terms as : a - d, a, a + d.
(2) = Four terms as : a - 3d, a - d, a + d, a + 3d.
(3) = Five terms as : a - 2d, a - d, a, a + d, a + 2d.