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if 9th term of AP is -32 and sum of 11th and 13th term is -94 . find the common difference of an AP .

Posted by Ilma Parvez 6 years, 4 months ago

CBSE > Class 10 > Mathematics

2 answers

Sia ? 6 years, 4 months ago

Let the first term and common difference of an A.P. be a & d respectively.
n^th term of an A.P. is a_n = a + (n -1)d
Given that,

a₉= -32
{tex}\Rightarrow{/tex} a+8d= -32...(i)
Also given,
a₁₁+a₁₃= -94
{tex}\Rightarrow{/tex} (a + 10d) + (a + 12d) = -94
{tex}\Rightarrow{/tex} 2a + 22d = -94
{tex}\Rightarrow{/tex} a + 11d = -47...(ii)
Subtracting (i) from (ii).
11d - 8d = -47 - (-32)

Or, 3d = -47+32

Or, 3d = - 15
Or, d = -5
So, the common difference is -5.

1Thank You

Fun And Music Adda 6 years, 4 months ago

Common difference= -5

2Thank You

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