Advertisements
Advertisements
प्रश्न
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Advertisements
उत्तर
Given that,
a = 17
l = 350
d = 9
Let there be n terms in the A.P.
l = a + (n − 1) d
350 = 17 + (n − 1)9
9n = 350 + 9 - 17
9n = 359 - 17
9n = 342
⇒ n = `342/9`
⇒ n = 38
Sn = `n/2(a+l)`
Sn = `38/2(17+350)`
= 19 × 367
= 6973
Thus, this A.P. contains 38 terms and the sum of the terms of this A.P. is 6973.
APPEARS IN
संबंधित प्रश्न
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
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)]
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Find the sum of all integers between 50 and 500, which are divisible by 7.
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
Find the middle term of the AP 10, 7, 4, ……., (-62).
Determine k so that (3k -2), (4k – 6) and (k +2) are three consecutive terms of an AP.
Find the three numbers in AP whose sum is 15 and product is 80.
Divide 24 in three parts such that they are in AP and their product is 440.
If the numbers (2n – 1), (3n+2) and (6n -1) are in AP, find the value of n and the numbers
What is the 5th term form the end of the AP 2, 7, 12, …., 47?
How many terms of the AP 63, 60, 57, 54, ….. must be taken so that their sum is 693? Explain the double answer.
Find the sum of all multiples of 9 lying between 300 and 700.
The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
Simplify `sqrt(50)`
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?
If the first term of an A.P. is a and nth term is b, then its common difference is
If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is
If the third term of an A.P. is 1 and 6th term is – 11, find the sum of its first 32 terms.
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.
Find the sum of first 1000 positive integers.
Activity :- Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `square`
S1000 = `square/2 (1 + 1000)`
= 500 × 1001
= `square`
Therefore, Sum of the first 1000 positive integer is `square`
Find the sum of numbers between 1 to 140, divisible by 4.
Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
Find the sum of first 'n' even natural numbers.
