Advertisements
Advertisements
Question
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
Solution
We have been given an A.P
2+6+10+...+x=1800
a = 2, d = 6 - 2 = 4, `a_n = x "and" s_n = 1800`
Firstly, we will find using
`S_n = n/2[2a + (n - 1)d]`
`1800 = n/2[2 xx 2 + (n - 1)4]`
`1800 = (4n + 4n^2 - 4n)/2`
`900 = n^2`
⇒ n = ±30
Number of terms can not be negative
n = 30
Now for value of x which is `a_n`
`a_n = a + (n - 1)d`
`x = 2 + (30 - 1)4`
x = 2 + 116
x = 118
APPEARS IN
RELATED QUESTIONS
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, ... to 25 terms
What is the 5th term form the end of the AP 2, 7, 12, …., 47?
Choose the correct alternative answer for the following question .
What is the sum of the first 30 natural numbers ?
Find the sum of the first 15 terms of each of the following sequences having nth term as xn = 6 − n .
If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is
Sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.
Find the sum of numbers between 1 to 140, divisible by 4
In an AP if a = 1, an = 20 and Sn = 399, then n is ______.
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
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?
