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If sum of n terms is given by S_{n} = 3n^{2} + 5n, then the common difference of this AP is:
We know S1is the sum of 1st term which is a
S_{1 }= 3 + 5 = 8 = a
S_{2} is sum of first two terms
S_{2}=3 * 4 + 5 * 2 = 12 + 10 = 22
And We have a_{2}= S_{2}  S_{1} = 22  8 = 14
d = a_{2 }a_{1 }= 14  8 = 6
An athlete wants to improve his stamina, so he decides to increase the distance he runs by half a kilometer every day. If he starts with 5 km on first day, find how much he runs on the 10 th day
Distance increased every day is the common difference for the AP which is 0.5
Initial distance is 5 km , so a=5
To find the distance at 10th day, so n=10
l=a+(n1)d
=5+(101)0.5
=5+4.5=9.5km
A tree in each year grows 4cm less than it grew in previous year. If it grew 1 metre in the first year, in how many years will it have ceased growing and what will be its height then,
One metre = 100 cm, a = 100 cm
since every year it grows 4 cm less than it did the preceding year, d = 4
Thus, it is an AP, with initial term a = 100 and d = 4
The tree will stop its growth, when nth term of the series is 0.
Nth term = a + (n  1)d
0 = 100 + (n  1)(4)
0 = 100  4n + 4
0 = 104 4n
4n = 104
n = 104/4
n = 26 years
Which term of the A.P 10,8,6,… will be the first negative term?
During the festival season , a girl wants to prepare a design at the entrance to her house. The pattern is such that starting with one dot she wants to go on increasing the number of dots by 3 every time. In which row will she have 55 dots?
Find the fifth term of an A.P whose first term is 1 and common difference is 3
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