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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 3n^{2}+5n then which of its terms is 164?

Solution:

Sn=3n^{2}+5n

S_{1}=a_{1}=3(1)^{2}+5(1)=8

S_{2}=3(2)^{2}+5(2)=22

S_{2}=22=a_{1}+a_{2}

a_{2}=22-8=14

d=a_{2}-a_{1}=14-8=6

n^{th} term value is 164,then what is n?

n^{th }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 27^{th}term is 164.

QUESTION: 7

For an A.P. t_{n }= 2n+3, what is the formula for S_{n}?

Solution:

Given , t_{n} = 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.S_{n} = n^{2} + 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:

S_{n} = 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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