Advertisements
Advertisements
प्रश्न
The sum of the first n terms of an AP is given by `s_n = ( 3n^2 - n) ` Find its
(i) nth term,
(ii) first term and
(iii) common difference.
उत्तर
Given : `s_n = ( 3n^2 - n) ` .............(1)
Replacing n by (n - 1) in (i), we get:
`s_(n-1) = 3 (n-1) ^2 - (n-1)`
= 3 (n2 - 2n +1 ) - n + 1
= 3n2 -7 n + 4
(i) Now , `T_n = ( s_n - s_( n-1))`
`=(3n^2 - n) - ( 3n^2 - 7n +4) = 6n -4 `
∴ nth term , Tn = (6n -4) ..................(ii)
(ii) Putting n = 1 in (ii), we get:
`T_1 = (6 xx 1) -4 = 2`
(iii) Putting n = 2 in (ii), we get:
`T_2 = (6xx 2 )-4 = 8`
∴ Common difference, d = T2 - T1 = 8 - 2 = 6
APPEARS IN
संबंधित प्रश्न
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Find the sum of first 40 positive integers divisible by 6.
Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.
The 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94. Find the common difference of the AP.
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
Find the sum \[7 + 10\frac{1}{2} + 14 + . . . + 84\]
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
If \[\frac{5 + 9 + 13 + . . . \text{ to n terms} }{7 + 9 + 11 + . . . \text{ to (n + 1) terms}} = \frac{17}{16},\] then n =
Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h–1. The second car goes at a speed of 8 km h–1 in the first hour and thereafter increasing the speed by 0.5 km h–1 each succeeding hour. After how many hours will the two cars meet?
