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Test: Word Problems of AP


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Test: Word Problems of AP - Question 1

If sum of n terms is given by Sn = 3n2 + 5n, then the common difference of this AP is:

Detailed Solution for Test: Word Problems of AP - Question 1

We know S1is the sum of 1st term which is a
S= 3 + 5 = 8 = a
S2 is sum of first two terms
S2=3 * 4 + 5 * 2 = 12 + 10 = 22  
And We have a2= S2 - S1 = 22 - 8 = 14
d = a-a= 14 - 8 = 6 

Test: Word Problems of AP - Question 2

What is the sum of the first 50 multiples of 3?​

Test: Word Problems of AP - Question 3

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

Detailed Solution for Test: Word Problems of AP - Question 3

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+(n-1)d
 =5+(10-1)0.5
 =5+4.5=9.5km

Test: Word Problems of AP - Question 4

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,​

Detailed Solution for Test: Word Problems of AP - Question 4

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

Test: Word Problems of AP - Question 5

If Ss = 32, S4 = 28 ~~ What is t=?

Test: Word Problems of AP - Question 6

How many terms are there in 20, 25, 30......... 140

Test: Word Problems of AP - Question 7

Which term of the A.P 10,8,6,… will be the first negative term?

Test: Word Problems of AP - Question 8

Find the sum of first 40 integers divisible by 6​

Test: Word Problems of AP - Question 9

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?

Test: Word Problems of AP - Question 10

Find the fifth term of an A.P whose first term is -1 and common difference is -3

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