Test: nth Term of AP


20 Questions MCQ Test Mathematics (Maths) Class 10 | Test: nth Term of AP


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QUESTION: 1

The common difference of an A.P. in which a25 – a12 = -52 is:

Solution:

We have an = a+(n-1)d
a25 = a+(25-1)d=a+24d
a12 = a+(12-1)d=a+11d
a25 - a12 = -52
a+24d-(a+11d)=-52
a+24d-a-11d=-52
13d= -52
d= -4

QUESTION: 2

The number of two digit numbers divisible by 5 is

Solution:

Highest two digit number divisible by 5 is 95
l=95, a=10 and d=5
l=a+(n-1)d
95=10+(n-1)5
(n-1)5=85
n-1=17
n=18

QUESTION: 3

Which term of the A.P. 1, 4, 7 … is 88?

Solution:
A+(n-1)d here a=1 and d=3 1+(n-1)3=88 1+3n-3)=88 -2+3n=88 3n=88+2 3n=90 so n=90/3 n=30.
QUESTION: 4

The 12th term of the A.P. with first term 1/2 and common difference 1/12 is …​

Solution:
QUESTION: 5

The common difference and the next two terms of the A.P are….

Solution:

Common difference=¼-0=½-¼=¼
Next term =¾+¼=1
Next term =1+¼=5/4

QUESTION: 6

The next term of the given series  would be

Solution:

We have an AP : 
Here a= 
l=a+(n-1)d

QUESTION: 7

The common difference of the A.P for which 20th term is 10 more than the 18th term is :

Solution:
QUESTION: 8

The common difference of the AP for which 20th term is 10 more than the 18th term is:

Solution:
QUESTION: 9

The nth term of the AP 9, 13, 17, 21, 25, ………….. is:​

Solution:
QUESTION: 10

The common difference and the next two terms of the A.P are….1.8, 2.0, 2.2, 2.4,….​

Solution:
QUESTION: 11

The first negative term of the sequence 114, 109, 104 ………… is

Solution:

l=a+(n-1)d , d=109-114=-5
First negative term will be
0 > a+(n-1)d
0 > 114+(n-1)(-5)
0 > 114-5n+5
5n > 119
n > 119/5=23.8
So the first negative term will be 24th term.

QUESTION: 12

The common difference and the next two terms of the A.P are…. 75, 67, 59, 51,……​

Solution:
QUESTION: 13

If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is       

Solution:

QUESTION: 14

15th term of the A.P. x – 7, x – 2, x + 3 … is:​

Solution:

The given AP is x – 7, x – 2, x + 3 …
So a= x-7, d=x - 2- x + 7 = x + 3 - x +2 = 5
l = a + (n - 1)d
=x - 7 + (15 - 1)5
=x - 7 + 70 = x + 63

QUESTION: 15

Which term of A.P. 5, 13, 21, is 189

Solution:
QUESTION: 16

Which term of the A.P. 63, 84, …… is 399?​

Solution:

The correct answer is b

  A=21

d=21

 a_{n} =420

n=?

 a_{n} =a+(n-1)d

420=21+(n-1)21

(n-1)*21=399

n-1=399/21

n-1=19

n=19+1=20

therefore the 20th term of the AP is 420

QUESTION: 17

In given AP 210 is …………. th term of: 2,6,10……..​

Solution:

We have a=2, d=6-2=4
l=a+(n-1)d
210=2+(n-1)4
208/4=n-1
n=53rd term

QUESTION: 18

How many terms are there in the AP 7, 13, 19, 25…205

Solution:

The sequence is an arithmetic sequence

The nth term of an AP is given by:

APn = a + d(n - 1)

a = first term = 7

d = common ratio = 13 - 7 = 6 or 19 - 13 = 6 or 25 - 19 = 6

205 = 7 + 6(n - 1)

6(n - 1) = 198

n - 1 = 33

n = 34

The sequence has 34 terms.

QUESTION: 19

The 11th term of 10.0, 10.5, 11.0, 11.5, ……is…​

Solution:

We have an AP :10.0, 10.5, 11.0, 11.5
Where a=10, d=0.5
l=a+(n-1)d
 =10+(11-1)0.5
 =10+5=15

QUESTION: 20

The 9th term of   is…​

Solution:

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