Question

if the 3rd and 9th term of an AP are 4 and-8 respectively which term of the Ap is zero
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Answer 1

GIVEN:

• 3rd term = 4
• 9th term = -8

TO FIND:

• Which term of an A.P. is zero ?

SOLUTION:

3rd Term = a + 2d

9th term = a + 8d

• a + 2d = 4...1)
• a + 8d = -8....2)

From equation 1)

$\rm{\dashrightarrow a = 4 -2d }$

Put the value of a in equation 2)

$\rm{\dashrightarrow (4 -2d) +8d = -8}$

$\rm{\dashrightarrow 4-2d +8d = -8 }$

$\rm{\dashrightarrow 4 + 6d = -8 }$

$\rm{\dashrightarrow 6d = -8 -4 }$

$\rm{\dashrightarrow 6d = -12}$

$\rm{\dashrightarrow d = \cancel\dfrac{-12}{6} }$

$\bf{\dashrightarrow d = -2 }$

Put the value of d in equation 1)

$\rm{\dashrightarrow a = 2 \times -2 = 4 }$

$\rm{\dashrightarrow a = 4 +4}$

$\bf{\dashrightarrow a = 8 }$

Now, we have given that

• First term (a) = 8
• Common difference (d) = -2
• Last term (l) = 0

$\large{\boxed{\bf{ a_n = a + (n - 1) d}}}$

$\rm{\dashrightarrow 0 = 8 +(n-1) -2 }$

$\rm{\dashrightarrow 0 = 8 -2n +2 }$

$\rm{\dashrightarrow 0 = -2n + 10 }$

$\rm{\dashrightarrow 2n = 10 }$

$\rm{\dashrightarrow n = \dfrac{10}{2} }$

$\bf{\dashrightarrow n = 5 }$

❝ Hence, 5th term of an A.P is 0 ❞

______________________

Answer 2

Answer:

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