Test: Sum of n Terms of AP


10 Questions MCQ Test Mathematics (Maths) Class 10 | Test: Sum of n Terms of AP


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QUESTION: 1

What is the sum of the first 20 whole numbers?​

Solution:

First 20 whole numbers are: 0-19.

Their sum = 0+1 +2+3+4+5+ 6+7+8+9+9+10+11+12+13+14 +15+16+17+ 18+19 = 190

QUESTION: 2

The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

Solution:
QUESTION: 3

For an A.P the sum of first 30 terms is -1155,the common difference is -3and the thirtieth term is -82. What is the first term?

Solution:

l = a + (n - 1)d
Where l = -82,a = ?,d = -3,n = 30
-82 = a + 29 (- 3)
a = 5

QUESTION: 4

Find the sum of the first 15 multiples of 8.

Solution:
QUESTION: 5

How many terms of AP 54, 51, 48… are required to give a sum of 513?​

Solution:
QUESTION: 6

If the sum of n terms of an AP is 3n2+5n then which of its terms is 164?​

Solution:

Sn=3n2+5n

S1=a1=3(1)2+5(1)=8

S2=3(2)2+5(2)=22

S2=22=a1+a2

a2=22-8=14

d=a2-a1=14-8=6

nth term value is 164,then what is n?

nth term=a+(n-1)d

164=8+(n-1)6

164-8 / 6=n-1

156/6=n-1

26+1=n

n=27

So 27thterm is 164.

QUESTION: 7

For an A.P. t= 2n+3, what is the formula for Sn?​

Solution:

Given , tn = 2n+3
t1=2×1+3
t1=5
Sn=n/2(t1+tn)
=n/2 (5+2n+3)
=n/2(2n+8)
=n(n+4)

QUESTION: 8

If for an A.P.Sn = n2 + 3n What is the n th term?​

Solution:
QUESTION: 9

What is the sum of the first 25 terms of the A.P -10,-7,-4,…….?​

Solution:

Sn = n/2[a+(n-1)d]
= 25/2[-10+(25-1)3]
= 25/2[-10+72]
= 25/2[62]
= 25*31
= 775

QUESTION: 10

The sum of the first n terms of an A.P. is 2235.The first term is 2 and the common difference is 5. What is n = ?

Solution:

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