Advertisements
Advertisements
प्रश्न
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Advertisements
उत्तर
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n =n/2 [2a + (n -1)d]`
Where a = first term for the given A.P.
d = common difference of the given A.P
n = number of terms
50, 46, 42, ... to 10 terms
Common difference of the A.P. (d)
`= a_2 - a_1`
= 46 - 50
= -4
Number of terms (n) = 10
First term for the given A.P. (a) = 50
So using the formula we get
`S_10 = 10/2 [2(50) + (10 - 1)(-4)]`
= (5)[100 + (9)(-4)]
= (5)[100 - 36]
= (5)[64]
= 320
Therefore the sum of first 10 terms for the given A.P is 320
APPEARS IN
संबंधित प्रश्न
If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
Find the sum of first 15 multiples of 8.
Find how many integers between 200 and 500 are divisible by 8.
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Find the sum of all odd numbers between 100 and 200.
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
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.
A piece of equipment cost a certain factory Rs 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
If the sum of n terms of an A.P. is Sn = 3n2 + 5n. Write its common difference.
The common difference of an A.P., the sum of whose n terms is Sn, is
Q.19
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:
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
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))`.
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
