Advertisements
Advertisements
प्रश्न
The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.
Advertisements
उत्तर
First term a = 5
Last term l = 45
Sum of terms = 1000
Let there be n terms in this A.P.
Now, sum of first n terms = `n/2 [a + l]`
`=> 1000 = n/2 [5 + 45]`
`=>` 2000 = n × 50
`=>` n = 40
l = a + (n – 1)d
`=>` 45 = 5 + (40 – 1)d
`=>` 40 = 39d
`=> d = 40/39`
Hence, number of terms are 40 and common difference is `40/39`.
संबंधित प्रश्न
Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120
Find the sum of the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
The first term of an AP is p and its common difference is q. Find its 10th term.
In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.
For an A.P., If t1 = 1 and tn = 149 then find Sn.
Activitry :- Here t1= 1, tn = 149, Sn = ?
Sn = `"n"/2 (square + square)`
= `"n"/2 xx square`
= `square` n, where n = 75
Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4.
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
The sum of 41 terms of an A.P. with middle term 40 is ______.
