Advertisements
Advertisements
प्रश्न
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
Advertisements
उत्तर
For this A.P.,
a = 7
l = 84
d = a2 − a1
= `10 1/2 - 7`
= `21/2 - 7`
= `7/2`
Let 84 be the nth term of this A.P.
l = a (n - 1)d
`84 = 7 + (n - 1) × 7/2`
`77 = (n - 1) × 7/2`
22 = n − 1
n = 23
We know that,
Sn = `n/2 (a + l)`
S23 = `23/2 [7 + 84]`
= `23/2xx91`
= `2093/2`
= `1046 1/2`
Thus, the required sum is `1046 1/2`.
APPEARS IN
संबंधित प्रश्न
The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Find the 6th term form the end of the AP 17, 14, 11, ……, (-40).
Determine the nth term of the AP whose 7th term is -1 and 16th term is 17.
Find the sum of the following Aps:
9, 7, 5, 3 … to 14 terms
How many terms of the AP 21, 18, 15, … must be added to get the sum 0?
Write an A.P. whose first term is a and common difference is d in the following.
a = –19, d = –4
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
If the sum of first n terms of an A.P. is \[\frac{1}{2}\] (3n2 + 7n), then find its nth term. Hence write its 20th term.
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
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
Q.10
Write the formula of the sum of first n terms for an A.P.
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 the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
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.
