The 13th term of an A.P. is 39 and the 23rd term is 69.find the 18th term of this A.P
Answers
EXPLANATION.
The 13th term of an ap = 39.
The 23rd term of an ap = 69.
As we know that,
General term of an A.P.
⇒ Tₙ = a + (n - 1)d.
Using this formula in the equation, we get.
The 13th term of an ap = 39.
⇒ T₁₃ = a + (13 - 1)d.
⇒ T₁₃ = a + 12d.
⇒ a + 12d = 39. - - - - - (1).
The 23rd term of an ap = 69.
⇒ T₂₃ = a + (23 - 1)d.
⇒ T₂₃ = a + 22d.
⇒ a + 22d = 69. - - - - - (2).
From equation (1) and (2), we get.
Subtract both equation (1) and (2).
⇒ a + 12d = 39. - - - - - (1).
⇒ a + 22d = 69. - - - - - (2).
⇒ - - -
We get,
⇒ - 10d = - 30.
⇒ d = 3.
Put the value of d = 3 in equation (1), we get.
⇒ a + 12d = 39.
⇒ a + 12(3) = 39.
⇒ a + 36 = 39.
⇒ a = 39 - 36.
⇒ a = 3.
First term = a = 3.
Common difference = d = b - a = 3.
To find : 18th term of an ap.
⇒ T₁₈ = a + (18 - 1)d.
⇒ T₁₈ = a + 17d.
Put the values in the equation, we get.
⇒ T₁₈ = 3 + 17(3).
⇒ T₁₈ = 3 + 51.
⇒ T₁₈ = 54.
18th term of an ap = 54.