Third term of an arthemetic sequence is 34 and 6th term is 67. a) find the common difference b) Find the first term
Answers
EXPLANATION.
3rd term of an A.P. = 34.
6th term of an A.P. = 67.
As we know that,
General terms of an A.P.
⇒ Tₙ = a + (n - 1)d.
⇒ T₃ = 34.
⇒ T₃ = a + (3 - 1)d.
⇒ T₃ = a + 2d.
⇒ a + 2d = 34. ⇒ (1).
⇒ T₆ = 67.
⇒ T₆ = a + (6 - 1)d.
⇒ T₆ = a + 5d.
⇒ a + 5d = 67. ⇒ (2).
From equation (1) & (2), we get.
⇒ a + 2d = 34.
⇒ a + 5d = 67.
We get,
⇒ - 3d = - 33.
⇒ d = 11.
Put the value of d = 11 in equation (1), we get.
⇒ a + 2d = 34.
⇒ a + 2(11) = 34.
⇒ a = 34 - 22.
⇒ a = 12.
First term = a = 12.
Common difference = d = 11.
MORE INFORMATION.
General terms of an A.P.
General term (nth term) of an A.P. is given by,
Tₙ = a + (n - 1)d.
Sum of n terms of an A.P.
Sₙ = n/2 [ 2a + (n - 1)d] Or Sₙ = n/2 [ a + Tₙ].
(1) = If sum of n terms Sₙ is given then general term Tₙ = Sₙ - Sₙ₋₁ where Sₙ₋₁ is sum of (n - 1) terms of A.P.
Answer:
Explanation :-
3rd term of an A.P. = 34.
6th term of an A.P. = 67.
As we know that,
General terms of an A.P.
⇒ Tₙ = a + (n - 1)d.
⇒ T₃ = 34.
⇒ T₃ = a + (3 - 1)d.
⇒ T₃ = a + 2d.
⇒ a + 2d = 34. ⇒ (1).
⇒ T₆ = 67.
⇒ T₆ = a + (6 - 1)d.
⇒ T₆ = a + 5d.
⇒ a + 5d = 67. ⇒ (2).
From equation (1) & (2), we get.
⇒ a + 2d = 34.
⇒ a + 5d = 67.
We get,
⇒ - 3d = - 33.
⇒ d = 11.
Put the value of d = 11 in equation (1), we get.
⇒ a + 2d = 34.
⇒ a + 2(11) = 34.
⇒ a = 34 - 22.
⇒ a = 12.
First term = a = 12.
Common difference = d = 11.
Learn more!!
General terms of an A.p. :-
General term (nth term) of an A.P. is given by,
Tₙ = a + (n - 1)d.
Sum of n terms of an A.P. :-
Sₙ = n/2 [ 2a + (n - 1)d] Or Sₙ = n/2 [ a + Tₙ].
(1) = If sum of n terms Sₙ is given then general term Tₙ = Sₙ - Sₙ₋₁ where Sₙ₋₁ is sum of (n - 1) terms of A.P.
Step-by-step explanation: