If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively. Which term of it is zero ?

Let first term be a and common difference be d. Given, ⇒ 3rd term = 4 ⇒ a 3 = 4 ⇒ a + 2d = 4 ⇒ a = 4 - 2d ........(Eq. 1) Given, ⇒ 9th term = -8 ⇒ a 9 = -8 ⇒ a + 8d = -8 ⇒ a = -8 - 8d ........(Eq. 2) From Eq. 1 and Eq. 2, ⇒ 4 - 2d = -8 - 8d ⇒ -2d + 8d = -8 - 4 ⇒ 6d = -12 ⇒ d = = -2. Substituting value of d in Eq. 1, we get : ⇒ a = 4 - 2d = 4 - 2(-2) = 4 + 4 = 8. Let nth term be zero. ⇒ a n = 0 ⇒ a + (n - 1)d = 0 ⇒ 8 + (n - 1)(-2) = 0 ⇒ 8 - 2n + 2 = 0 ⇒ 2n = 10 ⇒ n = = 5. Hence, 5th term will be 0.

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In the given figure, P(-3, -4) is the mid-point of the line segment AB.
Find the coordinates of points A and B. Also, find the equation of the line passing through the point P and also perpendicular to line-segment AB.

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A and B are two events such that P(A) = 0.56 and P(B) = 0.64, find :
(i) P(not A)
(ii) P(not B)

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Mathematics

If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively. Which term of it is zero ?

AP GP

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In the given figure, P(-3, -4) is the mid-point of the line segment AB.
Find the coordinates of points A and B. Also, find the equation of the line passing through the point P and also perpendicular to line-segment AB.

A and B are two events such that P(A) = 0.56 and P(B) = 0.64, find :
(i) P(not A)
(ii) P(not B)

Mathematics

If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively. Which term of it is zero ?

AP GP

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Find the coordinates of points A and B. Also, find the equation of the line passing through the point P and also perpendicular to line-segment AB.

A and B are two events such that P(A) = 0.56 and P(B) = 0.64, find :
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(ii) P(not B)