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This mock test of Test: Word Problems of AP for Class 10 helps you for every Class 10 entrance exam.
This contains 10 Multiple Choice Questions for Class 10 Test: Word Problems of AP (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If sum of n terms is given by S_{n} = 3n^{2} + 5n, then the common difference of this AP is:

Solution:

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

QUESTION: 2

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

Solution:

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

Solution:

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

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,

Solution:

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

QUESTION: 5

If S_{s} = 32, S_{4} = 28 ~~ What is t_{s }=?

Solution:

QUESTION: 6

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

Solution:

QUESTION: 7

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

Solution:

QUESTION: 8

Find the sum of first 40 integers divisible by 6

Solution:

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?

Solution:

QUESTION: 10

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

Solution:

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