Advertisements
Advertisements
Questions
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
The sum of the first 7 terms of an AP is 49 and the sum of its first 17 terms is 289. Find the sum of its first n terms.
Advertisements
Solution
Let the first term and the common difference of the given A.P. be a and d, respectively.
Sum of the first 7 terms, S7 = 49
We know
`S = n/2[2a + (n - 1)d]`
⇒ `7/2(2a + 6d) = 49`
⇒ `7/2 xx 2(a + 3d) = 49`
⇒ a + 3d = 7 ...(1)
Sum of the first 17 terms, S17 = 289
⇒ `17/2(2a + 16d) = 289`
⇒ `17/2 xx 2(a + 8d) = 289`
⇒ a + 8d = `289/17`
⇒ a + 8d = 17 ...(2)
Subtracting (2) from (1), we get
5d = 10
d = `5/10`
⇒ d = 2
Substituting the value of d in (1), we get
a = 1
Now,
sum of the first n terms is given by
`S_n = n/2[2a + (n - 1)d]`
= `n/2[2 xx 1 + (n - 1) xx 2]`
= `n/2 [2 + 2n - 2]`
= `n/2 [2n]`
= n2
Therefore, the sum of the first n terms of the A.P. is n2.
APPEARS IN
RELATED QUESTIONS
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees, and so on till class XII. There are three sections of each class. How many trees will be planted by the students?
200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed, and how many logs are in the top row?
If an denotes the nth term of the AP 2, 7, 12, 17, ..., find the value of (a30 - a20).
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
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 = ....
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?
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.
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
