Question

If the 3rd and 9th term of an AP are 4 and -8 respectively, which term of this AP is zero?​

Answer 1

Answer:

7 th term

Step-by-step explanation:

T3=4 T9=-8

Ap is 6,5,4,3,2,1,0,-1,-2,-3,-4,-5,-6,-7,-8

Answer 2

QUESTION:

If the 3rd and 9th term of an AP are 4 and -8 respectively, which term of this AP is zero?

FORMULA USED :

$</u><u>\</u><u>h</u><u>u</u><u>g</u><u>e</u><u>\</u><u>p</u><u>u</u><u>r</u><u>p</u><u>l</u><u>e</u><u> </u><u>{</u><u>nth \: term = a + (n - 1)d</u><u>}</u><u>$

where;

a = first term

d = common difference

GIVEN :

$t3 = 4$

$t9 = - 8$

TO FIND :

Which term of the AP will be zero?

ANSWER:

$t3 = 4 \\ a + (3 - 1)d = 4 \\ a + 2d = 4....(eq.1)$

$t9 = - 8 \\ a + (9 - 1)d = - 8 \\ a + 8d = - 8...(eq.2)$

Subtracting eq 1 and equation 2;

$(a + 2d) - (a + 8d) = 4 - ( - 8) \\ a + 2d - a - 8d = 4 + 8 \\ - 6d = 12 \\ d = - 2$

Common difference = -2.

putting the value of d in eq 1;

$a + 2( - 2) = 4 \\ a - 4 = 4 \\ a = 8$

First term = 8

now,

$t(n) = 8 + (n - 1) - 2 \\ 0 = 8 - 2n + 2 \\ 0 = 10 - 2n \\ - 10 = - 2n \\ 5 = n$

FINAL ANSWER :

$</strong><strong>\</strong><strong>huge</strong><strong>\</strong><strong>blue</strong><strong> </strong><strong>{</strong><strong>5th \: term \: is \: 0</strong><strong>}</strong><strong>$