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`.
APPEARS IN
संबंधित प्रश्न
Find how many integers between 200 and 500 are divisible by 8.
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference.
How many two-digits numbers are divisible by 3?
The angles of a quadrilateral are in AP whose common difference is 10°. Find the angles.
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
Write the nth term of the \[A.P. \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
Q.11
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
