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प्रश्न
The 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94. Find the common difference of the AP.
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उत्तर
Let a be the first term and d be the common difference of the AP. Then,
a9 = - 32
⇒ a +(9-1) d= -32 [an = a + (n-1) d]
⇒ a + 8d = -32 ............(1)
Now ,
`a_11 + a_13 = -94` (Given)
`⇒ ( a +10d ) +( a + 12d) = -94`
⇒ 2a + 22d = -94
⇒ a+ 11d = -47 ...............(2)
From (1) and (2), we get
-32 -8d + 11d=-47
⇒ 3d = -47 + 32 =-15
⇒ d = -5
Hence, the common difference of the AP is - 5.
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