Question

The ninth termvof an ap is -32 and the sum of it eleventh term and thirteenth term is -94 .find the common difference of an ap

Answer 1

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Hey there !!


Given :-

$\large \bf{ = > a\tiny{9} }= - 32.$


And,


$\bf \large {= > a \tiny{11} } +{ a \tiny{13}} = - 94.$

▶ Find the value of common difference (d).



Solution :-)


we have ,

$\large \bf{ = > a\tiny{9} }= - 32.$


=> a + 8d = -32............(1).



▶ And,


$\bf \large {= > a \tiny{11} } +{ a \tiny{13}} = - 94.$


=> a + 10d + a + 12d = -94.

=> 2a + 22d = -94.

=> 2( a + 11d ) = -94.

=> a + 11d = -47..............(2).


▶ Substracte equation (1) and (2),


a + 8d = -32.
a +11d = -47.
(-)..(-)......(+)
__________


=> -3d = 15.


=> d = $\bf{ \frac{15}{-3} }$


$\huge \boxed{ => d = -5. }$



✔✔ Hence, the value of common difference (d) is founded ✅✅.

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Answer 2

a9= - 32.
a + 8d = -32..........1

a11+a13 = - 94.


=> a + 10d + a + 12d = -94.

=> 2a + 22d = -94.

=> a + 11d = -47.........2

Substracte eq 1 and 2, we get

-3d = 15.
d = 15/-3
d = -5.