Advertisements
Advertisements
प्रश्न
If the sum of first m terms of an AP is ( 2m2 + 3m) then what is its second term?
Advertisements
उत्तर
Let Sm denotes the sum of first m terms of the AP.
∴ sm = 2m2 +3m
`⇒ s_(m-1) = 2 (m -1)^2 +3 (m-1) = 2( m^2 - 2m +1) +3 (m-1) = 2m^2 - 3-1`
Now,
`m^(th) "term of A"P, a_m = s_m - s_(m-1)`
∴ `a_3 = ( 2m^2 + 3m ) - (2m^2 - m -1 ) = 4m +1`
Putting m = 2,we get
`a_2 = 4 xx 2 +1 = 9`
Hence, the second term of the AP is 9.
APPEARS IN
संबंधित प्रश्न
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
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?
Find the sum of first 8 multiples of 3
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of all integers between 50 and 500, which are divisible by 7.
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.
(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
Q.15
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
If a = 6 and d = 10, then find S10
Find S10 if a = 6 and d = 3
Find the sum of odd natural numbers from 1 to 101
If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be ______.
Find the sum:
1 + (–2) + (–5) + (–8) + ... + (–236)
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
