Test: nth Term of AP - Class 10 MCQ

# Test: nth Term of AP - Class 10 MCQ

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Test: nth Term of AP - Question 1

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

Detailed Solution for Test: nth Term of AP - Question 1

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

Test: nth Term of AP - Question 2

### The number of two digit numbers divisible by 5 is

Detailed Solution for Test: nth Term of AP - Question 2

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

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Test: nth Term of AP - Question 3

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

Detailed Solution for Test: nth Term of AP - Question 3
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.
Test: nth Term of AP - Question 4

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

Test: nth Term of AP - Question 5

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

Detailed Solution for Test: nth Term of AP - Question 5

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

Test: nth Term of AP - Question 6

The next term of the given series  would be

Detailed Solution for Test: nth Term of AP - Question 6

We have an AP :
Here a=
l=a+(n-1)d

Test: nth Term of AP - Question 7

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

Detailed Solution for Test: nth Term of AP - Question 7

Test: nth Term of AP - Question 8

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

Test: nth Term of AP - Question 9

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

Test: nth Term of AP - Question 10

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

Test: nth Term of AP - Question 11

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

Detailed Solution for Test: nth Term of AP - Question 11

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.

Test: nth Term of AP - Question 12

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

Test: nth Term of AP - 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

Detailed Solution for Test: nth Term of AP - Question 13

Test: nth Term of AP - Question 14

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

Detailed Solution for Test: nth Term of AP - Question 14

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

Test: nth Term of AP - Question 15

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

Test: nth Term of AP - Question 16

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

Detailed Solution for Test: nth Term of AP - Question 16

A=21

d=21

=420

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

Test: nth Term of AP - Question 17

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

Detailed Solution for Test: nth Term of AP - Question 17

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

Test: nth Term of AP - Question 18

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

Detailed Solution for Test: nth Term of AP - Question 18

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.

Test: nth Term of AP - Question 19

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

Detailed Solution for Test: nth Term of AP - Question 19

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

Test: nth Term of AP - Question 20

The 9th term of   is…​

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