Advertisements
Advertisements
प्रश्न
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
Advertisements
उत्तर
Given that S4 = 40 and S14 = 280'
`"S"_"n" = "n"/2[2"a" + ("n-1)d"]`
`"S"_4 = 4/2[2"a" + (4-1)"d"] = 40`
`=> 2"a" + 3"d" = 20` .......(i)
`"S"_14 = 14/2 [2"a" + (14 -1)"d"] = 280`
`=> 2"a" + 13"d" = 40` ...(ii)
(ii) - (i)
10d = 20 ⇒ d = 2
Sunstituting the value of d in (i) we get
2a + 6 = 20 ⇒ a = 7
Sum of first n terms,
`"S"_"n" = "n"/2[2"a" + ("n-1)d"]`
= `"n"/2 [14 + ("n"-1) 2]`
= n ( 7 + n - 1)
= n (n + 6)
= n2 + 6n
Therefore, Sn = n2 + 6n
संबंधित प्रश्न
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
If the common differences of an A.P. is 3, then a20 − a15 is
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =
If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.
Find the sum of three-digit natural numbers, which are divisible by 4
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
