Advertisements
Advertisements
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.
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.
APPEARS IN
संबंधित प्रश्न
The ratio of the sum use of n terms of two A.P.’s is (7n + 1) : (4n + 27). Find the ratio of their mth terms
A sum of ₹2800 is to be used to award four prizes. If each prize after the first is ₹200 less than the preceding prize, find the value of each of the prizes
If (2p +1), 13, (5p -3) are in AP, find the value of p.
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is
Q.15
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are ______.
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
