Advertisements
Advertisements
प्रश्न
In an AP, given a = 7, a13 = 35, find d and S13.
In an A.P. (with usual notations): given a = 7, a13 = 35, find d and S13.
Advertisements
उत्तर
Given that, a = 7, a13 = 35
As an = a + (n − 1) d,
∴ a13 = a + (13 − 1) d
35 = 7 + 12d
35 − 7 = 12d
28 = 12d
d = `28/12`
d = `7/3`
sn = `n/2[a+a_n]`
S13 = `n/2[a+a_13]`
= `13/2[7+35]`
= `(13xx42)/2`
= 13 × 21
= 273
संबंधित प्रश्न
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
Find the sum of first 40 positive integers divisible by 6.
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)]
If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the sum of first n odd natural numbers
Find the sum 2 + 4 + 6 ... + 200
Which term of the AP 21, 18, 15, …… is -81?
The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
If an denotes the nth term of the AP 2, 7, 12, 17, … find the value of (a30 - a20 ).
Write an A.P. whose first term is a and common difference is d in the following.
a = –3, d = 0
Choose the correct alternative answer for the following question .
If for any A.P. d = 5 then t18 – t13 = ....
There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
The sum of first 20 odd natural numbers is
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.
How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.
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`
In a ‘Mahila Bachat Gat’, Sharvari invested ₹ 2 on first day, ₹ 4 on second day and ₹ 6 on third day. If she saves like this, then what would be her total savings in the month of February 2010?
If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be ______.
The sum of first 16 terms of the AP: 10, 6, 2,... is ______.
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
