Question

The third term of a.p in -8 and the 9th term is 4 then 12th term is

Answer 1

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

=> The third term of an AP is - 8 and the 9th term is 4, Then the 12th term is ?

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$\mathcal{\huge{\underline{\underline{\red{Solution:-}}}}}$

The nth term of an AP can be calculated by using the formula

T(n) = a + (n - 1)d

Third term of an AP is - 8

- 8 = a + (- 8 - 1)d

=> - 8 = a - 9d ____1)

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Ninth term is 4

4 = a + (4 - 1)d

=> 4 = a + 3d ____2)

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Subtract equation 1) from equation 2)

4 - (-8) = (a + 3d) - (a - 9d)

=> 4 + 8 = a + 3d - a + 9d

=> 12 = 12d

=> d = 12/12

=> d = 1

Hence , common difference of the AP is 1

Put the value of d = 1 in the 2nd equation :-

4 = a + 3d

=> 4 = a + 3(1)

=> 4 = a + 3

=> a = 4 - 3

=> a = 1

Hence, first term of the AP is 1

T12 = a + (n - 1)d

=> T12 = 1 + (12 - 1)1

=> T12 = 1 + 11

=> T12 = 12

Hence, the value of 12th term is 12.

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