Advertisements
Advertisements
प्रश्न
The sum of first n terms of a certain series is given as 2n2 – 3n. Show that the series is an A.P.
उत्तर
Given Sn = 2n2 – 3n
S1 = 2(1)2 – 3(1) = 2 – 3 = – 1
⇒ t1 = a = – 1
S2 = 2(22) – 3(2) = 8 – 6 = 2
t2 = S2 – S1 = 2 – (– 1) = 3
∴ d = t2 – t1 = 3 – (– 1) = 4
Consider a, a + d, a + 2d, ….….
– 1, – 1 + 4, – 1 + 2(4), …..…
– 1, 3, 7, ….
Clearly, this is an A.P. with a = – 1, and d = 4.
APPEARS IN
संबंधित प्रश्न
Find the sum of the following
3, 7, 11, … up to 40 terms
Find the sum of the following
102, 97, 92, … up to 27 terms.
How many consecutive odd integers beginning with 5 will sum to 480?
The 104th term and 4th term of an A.P. are 125 and 0. Find the sum of first 35 terms
Raghu wish to buy a laptop. He can buy it by paying ₹ 40,000 cash or by giving it in 10 installments as ₹ 4800 in the first month, ₹ 4750 in the second month, ₹ 4700 in the third month and so on. If he pays the money in this fashion, find total amount paid in 10 installments
Raghu wish to buy a laptop. He can buy it by paying ₹ 40,000 cash or by giving it in 10 installments as ₹ 4800 in the first month, ₹ 4750 in the second month, ₹ 4700 in the third month and so on. If he pays the money in this fashion, find how much extra amount that he has to pay than the cost?
A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step requires two bricks less than the previous step
How many bricks are required for the top most step?
A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step requires two bricks less than the previous step
How many bricks are required to build the stair case?
Find the sum `[("a" - "b")/("a" + "b") + (3"a" - 2"b")/("a" + "b") + (5"a" - 3"b")/("a" + "b") + ... "to" 12 "terms"]`
An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is
