Advertisements
Advertisements
प्रश्न
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
Advertisements
उत्तर
It is given that,
t10 = 46
t5 + t7 = 52
Now,
\[t_n = a + \left( n - 1 \right)d\]
\[ t_{10} = a + \left( 10 - 1 \right)d\]
\[ \Rightarrow 46 = a + 9d\]
\[ \Rightarrow a = 46 - 9d . . . \left( 1 \right)\]
\[ t_5 + t_7 = 52\]
\[ \Rightarrow \left( a + \left( 5 - 1 \right)d \right) + \left( a + \left( 7 - 1 \right)d \right) = 52\]
\[ \Rightarrow a + 4d + a + 6d = 52\]
\[ \Rightarrow 2a + 10d = 52\]
\[ \Rightarrow 2\left( 46 - 9d \right) + 10d = 52 \left( \text { from }\left( 1 \right) \right)\]
\[ \Rightarrow 92 - 18d + 10d = 52\]
\[ \Rightarrow 92 - 8d = 52\]
\[ \Rightarrow 8d = 92 - 52\]
\[ \Rightarrow 8d = 40\]
\[ \Rightarrow d = 5\]
\[ \Rightarrow a = 46 - 9\left( 5 \right) \left( \text { from }\left( 1 \right) \right)\]
\[ \Rightarrow a = 46 - 45\]
\[ \Rightarrow a = 1\]
Hence, the given A.P. is 1, 6, 11, 16, ....
APPEARS IN
संबंधित प्रश्न
Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....
Determine the nth term of the AP whose 7th term is -1 and 16th term is 17.
Divide 24 in three parts such that they are in AP and their product is 440.
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
Choose the correct alternative answer for the following question .
In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
What is the sum of first 10 terms of the A. P. 15,10,5,........?
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
The first term of an A.P. is p and its common difference is q. Find its 10th term.
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is
Q.6
Q.3
Q.6
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
Find the sum of odd natural numbers from 1 to 101
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a + c)(b + c - 2a))/(2(b - a))`
Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.
Reason (R): The sum of first n odd natural numbers is n2.
Read the following passage:
|
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. |
- In which year, the production is 29,200 sets?
- Find the production in the 8th year.
OR
Find the production in first 3 years. - Find the difference of the production in 7th year and 4th year.
