find the AP whose 6th term is 5 and the 13th term is -2
Answers
EXPLANATION.
The 6th term of an ap = 5.
The 13th term of an ap = - 2.
As we know that,
General term of an ap.
⇒ Tₙ = a + (n - 1)d.
Using this formula in the equation, we get.
The 6th term of an ap = 5.
⇒ T₆ = a + (6 - 1)d.
⇒ T₆ = a + 5d.
⇒ a + 5d = 5. - - - - - (1).
The 13th term of an ap = - 2.
⇒ T₁₃ = a + (13 - 1)d.
⇒ T₁₃ = a + 12d.
⇒ a + 12d = - 2. - - - - - (2).
From equation (1) and (2).
Subtract both the equation (1) and (2), we get.
⇒ a + 5d = 5. - - - - - (1).
⇒ a + 12d = - 2. - - - - - (2).
⇒ - - +
We get,
⇒ - 7d = 7.
⇒ d = - 1.
Put the value of d = - 1 in the equation (1), we get.
⇒ a + 5d = 5.
⇒ a + 5(-1) = 5.
⇒ a - 5 = 5.
⇒ a = 5 + 5.
⇒ a = 10.
First term = a = 10.
Common difference = d = b - a = - 1.
As we know that,
Series of an ap = a, a + d, a + 2d, . . . . .
Put the values in the equation, we get.
⇒ 10, [10 + (-1)], [10 + 2(-1)], . . . . .
Series = 10, 9, 8, . . . . .