Advertisements
Advertisements
Question
Find the sum: 1 + 3 + 5 + 7 + ... + 199 .
Advertisements
Solution
1 + 3 + 5 + 7 + ... + 199 .
Common difference of the A.P. (d) = `a_2 - a
_1`
= 3-1
= 2
So here,
First term (a) = 1
Last term (l) = 199
Common difference (d) = 2
So, here the first step is to find the total number of terms. Let us take the number of terms as n.
Now, as we know,
`a_n = a + ( n - 1)d`
So, for the last term,
199 = 1 + (n-1)2
199 = 1 + 2n - 2
199+1 = 2n
n = `200/2`
n = 100
Now, using the formula for the sum of n terms, we get
`S_n = 100/2 [2(1) + (100 - 1) 2 ]`
=50 [ 2 + (99) 2]
= 50 (2 + 198)
On further simplification, we get,
`S_n = 50(200)`
= 10000
Therefore, the sum of the A.P is `S_n = 10000 `
APPEARS IN
RELATED QUESTIONS
The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers
Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the nth week, her week, her weekly savings become Rs 20.75, find n.
Find the sum of the following APs:
2, 7, 12, ..., to 10 terms.
In an AP given d = 5, S9 = 75, find a and a9.
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum 25 + 28 + 31 + ….. + 100
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ..... is the first negative term?
Which term of the AP 21, 18, 15, … is zero?
Find the 25th term of the AP \[- 5, \frac{- 5}{2}, 0, \frac{5}{2}, . . .\]
Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
Choose the correct alternative answer for the following question .
In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....
The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.
If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
Find the sum of odd natural numbers from 1 to 101
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n)..
Find:
- its first term and common difference
- sum of its first 25 terms
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
