Advertisements
Advertisements
प्रश्न
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
Advertisements
उत्तर
0.6, 1.7, 2.8, …, to 100 terms
For this A.P.,
a = 0.6
d = a2 − a1
= 1.7 − 0.6
d = 1.1
n = 100
We know that
Sn = `n/2[2a+(n-1)d]`
S100 = `100/2[2(0.6)+(100 - 1)1.1]`
= 50[1.2 + (99) × (1.1)]
= 50[1.2 + 108.9]
= 50[110.1]
= 5505
Thus, the required sum of first 100 terms is 5505.
संबंधित प्रश्न
Find the sum of first 8 multiples of 3
Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.
If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?
Find the middle term of the AP 10, 7, 4, ……., (-62).
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
Find the sum of all natural numbers between 200 and 400 which are divisible by 7.
The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.
The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Write the nth term of an A.P. the sum of whose n terms is Sn.
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
The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is
Q.15
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
In an A.P. a = 2 and d = 3, then find S12
The sum of first n terms of the series a, 3a, 5a, …….. is ______.
Find the sum of first 16 terms of the A.P. whose nth term is given by an = 5n – 3.
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))`.
