Formula for Sum of n Terms of an AP

Q.

If a and d are the first term and the common difference of an AP, $S_n$ denotes the sum to n terms of an AP. If $S_n=Pn+Q{n}^2$, what are P and Q?

1. a = P + Q ; d = Q/2

2. a = P + Q ; d = Q

3. a = P - Q ; d = 2Q

4. a = P + Q ; d = 2Q

Q.

Find the sum of first $24$ terms of an AP whose $n^{th}$ term is given by $a_n=3+2n$.

1. 624

2. 564

3. 672

4. 568

Q.

Find the sum of 20 terms of the A.P. 1, 4, 7, 10, ......

1. 590

2. 600

3. 570

4. 580

Q. If the sum of p terms of an AP is qand the sum of q term is p, then the sum of p + qterms will be:

1. 0
2. p - q
3. p + q
4. -(p + q)

Q.

What is the sum to n terms of the following series: 2, 4, 6, 8, …, ( $n^{th}$ term)?

1. n(n+1)

2. n(n-1)

3. n×n

4. (n+1)(n+2)

Q.

Find the sum of all odd numbers between 0 and 50.

1. 625

2. 675

3. 700

4. 650

Q.

A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... What is the total length of such a spiral made up of thirteen consecutive semicircles?

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Q.

Find the sum : 34 + 32 + 30 + .... + 10

1. 300

2. 286

3. 310

4. 240

Q. The sum up to n terms of an AP with first term $a$, last term $l$ and common difference $d$ is

1. $\frac{n}{2}(2a+(n-1\left)d\right)$
2. $n(2a+(n-1\left)d\right)$
   
3. $\frac{n}{2}(a+l)$
   
4. $n(2a+(n-1\left)d\right)$

Q.

Find the difference between the sum of first 100 natural numbers and the sum of even numbers from 1 to 100.

1. 2200

2. 2400

3. 2500

4. 2700