Question

If the 3rd and 9th terms of and AP are 4 and -8 respectively. Find the fifth term of this AP​

Answer 1

Answer:

5th term is 16/3

Step-by-step explanation:

Please see the above image for better experience.

Answer 2

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$\large\cal{\underline{\underline{Given }}}$

3rd term = 4

9th term = -8

$\large\cal{\underline{\underline{To \: find }}}$

5th term

$\large\cal{\underline{\underline{Solution }}}$

The general form of A.P. is a, a+d, a+2d,…

1st term = a

2nd term = a+d

3rd term = a+2d…

$\therefore \: {3rd \: term = a + 2d} \\ 9th \: term = a + 8d$

a+2d = 4_______(1)

a+8d = -8_______(2)

Subtracting (1) and (2)

$a + \: \: 2d = 4 \\ \: \: \: \: \underline{ {}^{ \tiny{( - )}} a { + }^{\tiny{( - )}} 8d = { \small{- }}^{\tiny{( + )}}8} \\ \: \: \: \: \: \: \underline{0a - 6d = 12 \: \: \: \: \: \: \: \: \: }$

i.e., -6d = 12

$d = \frac{12}{ - 6} = - 2$

Apply d = -2 in (1)

a+2d = 4

a+2(-2) = 4

a + (-4) = 4

a = 4+4 = 8

So, now we know that a = 16 and d = -2

$5th \: term = a + 4d$

= 8 + 4(-2)

= 8 + (-8)

= 8 - 8

= 0

$\large\cal{\underline{\underline{Conclusion }}}$

5th term = 0