Advertisements
Advertisements
प्रश्न
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
उत्तर
In the given AP, let the first term be a and the common difference be d.
Then, Tn = a + (n-1) d
Now, we have:
T 10 = a + (10 - 1) d
⇒ a +9d =52 ...................(1)
T13 = a +(13-1) d = a +12d ........(2)
T17 = a+ (17 -1) d = a + 16d ..........(3)
But, it is given that T17 = 20 + T13
i.e ., a+ 16d = 20 + a + 12d
⇒ 4d = 20
⇒ d= 5
On substituting d = 5 in (1), we get:
a + 9 × 5 = 52
⇒ a = 7
Thus, a = 7 and d = 5
∴ The terms of the AP are 7,12,17,22,.........
APPEARS IN
संबंधित प्रश्न
In an AP given a = 3, n = 8, Sn = 192, find d.
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
How many two-digits numbers are divisible by 3?
The sum of the first n terms of an AP is given by `s_n = ( 3n^2 - n) ` Find its
(i) nth term,
(ii) first term and
(iii) common difference.
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
The sum of first 20 odd natural numbers is
Q.17
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
If ₹ 3900 will have to be repaid in 12 monthly instalments such that each instalment being more than the preceding one by ₹ 10, then find the amount of the first and last instalment
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.
