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
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Find how many integers between 200 and 500 are divisible by 8.
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
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 all integers between 50 and 500, which are divisible by 7.
How many two-digits numbers are divisible by 3?
If k,(2k - 1) and (2k - 1) are the three successive terms of an AP, find the value of k.
If the numbers a, 9, b, 25 from an AP, find a and b.
Find an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40.
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.
Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
Write the sum of first n even natural numbers.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
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.
Find t21, if S41 = 4510 in an A.P.
The first term of an AP of consecutive integers is p2 + 1. The sum of 2p + 1 terms of this AP is ______.
The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.
Sum of 1 to n natural number is 45, then find the value of n.
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
The sum of 40 terms of the A.P. 7 + 10 + 13 + 16 + .......... is ______.
