Find the A P whose 6 th term is 10 and 10 th term is 9
Answers
EXPLANATION.
6th terms of an A.P. = 10.
10th terms of an A.P. = 9.
As we know that,
General term of an A.P.
⇒ Tₙ = a + (n - 1)d.
6th terms of an A.P. = 10.
⇒ T₆ = a + (6 - 1)d.
⇒ T₆ = a + 5d.
⇒ a + 5d = 10. - - - - - (1).
10th terms of an A.P. = 9.
⇒ T₁₀ = a + (10 - 1)d.
⇒ T₁₀ = a + 9d.
⇒ a + 9d = 9. - - - - - (2).
From equation (1) & (2), we get.
Subtract equation (1) & (2), we get.
⇒ a + 5d = 10. - - - - - (1).
⇒ a + 9d = 9. - - - - - (2).
⇒ - - -
We get,
⇒ - 4d = 1.
⇒ d = - 1/4.
Put the value of d = - 1/4 in equation (1), we get.
⇒ a + 5d = 10.
⇒ a + 5(-1/4) = 10.
⇒ a + (-5/4) = 10.
⇒ a - 5/4 = 10.
⇒ a = 10 + 5/4.
⇒ a = (40 + 5)/4.
⇒ a = 45/4.
First term = a = 45/4.
Common difference = d = -1/4.
Series = a, a + d, a + 2d, a + 3d. . . . . .
Series = 45/4, (45/4 - 1/4), (45/4 + 2(-1/4)), (45 + (-3/4)). . . . .
Series = 45/4, 44/4, 43/4, 42/4. . . . .
MORE INFORMATION.
Supposition of terms in 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.