Advertisements
Advertisements
Question
Find the sum:
`4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms
Solution
Here, first term, a = `4 - 1/n`
Common difference,
d = `(4 - 2/n) - (4 - 1/n)`
= `(-2)/n + 1/n`
= `(-1)/n`
∵ Sum of n terms of an AP,
Sn = `n/2[2a + (n - 1)d]`
⇒ Sn = `n/2[2(4 - 1/n) + (n - 1)((-1)/n)]`
= `n/2{8 - 2/n - 1 + 1/n}`
= `n/2(7 - 1/n)`
= `n/2 xx ((7n - 1)/n)`
= `(7n - 1)/2`
APPEARS IN
RELATED QUESTIONS
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
If the mth term of an A.P. is 1/n and the nth term is 1/m, show that the sum of mn terms is (mn + 1)
The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.
Which term of the AP 21, 18, 15, …… is -81?
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
Three numbers in A.P. have the sum of 30. What is its middle term?
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.
