Advertisements
Advertisements
Question
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.
Advertisements
Solution
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
RELATED QUESTIONS
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
If Sn denotes the sum of first n terms of an A.P., prove that S30 = 3[S20 − S10]
Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........
Find the sum given below:
34 + 32 + 30 + ... + 10
In an AP given a = 3, n = 8, Sn = 192, find d.
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
Find the sum of first 8 multiples of 3
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
Which term of AP 72,68,64,60,… is 0?
Which term of the AP 21, 18, 15, …… is -81?
In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.
(Assume that three consecutive terms in A.P. are a – d, a, a + d).
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]
Which term of the sequence 114, 109, 104, ... is the first negative term?
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find:
- the production in the first year.
- the production in the 10th year.
- the total production in 7 years.
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.
