Relation between Sn, Terms and Middle Term

Q.

Four numbers are inserted between the numbers 4 and 39 such that an AP results. Which is the biggest of these four numbers?

1. 32

2. 33

3. 31

4. 30

Q.

Four numbers are in A.P. If their sum is 20 and the sum of their square is 120, then the middle terms are

1. 2, 4

2. 4, 6

3. 6, 8

4. 8, 10

Q.

Find the sum of the squares of the first n natural numbers.

1. $\frac{n(n+1)(n-1)}{6}$

2. $\frac{n(n+1)(2n+1)}{6}$

3. $\frac{n^2(n+1)}{6}$

4. $\frac{n(2n+1)}{6}$

Q. An AP has four terms. If its first and last terms are 1 and 5 respectively, then its sum is

1. 21
2. 24
3. 6
4. 12

Q. The sum of 9 terms of an AP will be , if the middle term of the AP is 10.

1. 90
2. 55
3. 45

Q.

Four numbers are in A.P. If their sum is 20 and the sum of their squares is 120, then the middle terms are

1. 2, 4

2. 4, 6

3. 6, 8

4. 8, 10

Q. The sum of all two digit odd numbers is:

Q.

A person deposited Rs. 5000 in his saving account. The amount is set to increase by $(\frac{1}{10}{)}_{th}$ of itself every two years. What would be the maturity amount (in Rs.) of investment after the $2^{nd}$, $4^{th}$, $6^{th}$ and $8^{th}$ year respectively? Are these in AP?

1. 500, 1000, 1500, 2000, Yes

2. 5500, 6000, 6500, 7000, No

3. 5500, 6050, 6655, 7320.5, No

4. 5000, 6000, 7000, 8000, Yes

Q. Find the sum of all two digit odd numbers.

Q. Find the middle term of the AP $10,7,4,...(-62)$

Q. Check whether $-150$ is a term of the AP : $11,8,5,\mathrm{2.....}$

Q. If 18 terms are inserted between 4 and 60 such that the resulting sequence is an AP, then the sum of the resulting AP is .

1. 360
2. 480
3. 640

Q.

The sum of all two digit odd numbers is:

1. 2530

2. 2475

3. 4905

4. 4950

Q.

In an AP which has $n$ terms, if we know the first and the last term, then we can find the sum of all the terms.

1. True

2. False

Q. The first term of an infinitely decreasing G.P. is unity and its sum is S. The sum of the squares of the terms of the progression is

1. $\frac{S}{2S-1}$
2. $\frac{S^2}{2S-1}$
3. $\frac{S}{2-S}$
4. $S^2$

Q. The sum to $200$ terms of the series $1+4+6+5+11+6+.....$ is

1. $29,800$
2. $29,600$
3. $30,200$
4. None of these

Q. If 18 terms are inserted between 4 and 60 such that the resulting sequence is an AP, then find the sum of resulting AP.

Q. In an AP which has n terms, if we know the first and the last term, then we can find the sum of all the terms.

1. False
2. True

Q. If $a(b-c)x^2+b(c-a)xy+c(a-b)y^2$ is a perfect square, then the quantities $a,b,c$ are in

1. H.P
2. A.P
3. G.P
4. None of these

Q. The sum of `n' terms of a finite AP is $\frac{13}{2}$ times the sum of its first and last terms. Which term would be the middle term in this AP?

1. 7th term
2. 9th term
3. 5th term
4. 3rd term

Q. Is it an AP?
$1,4,7,10,13,16,19,22,25,...$

1. Yes
   
2. No
   
3. Ambiguous
   
4. Data insufficient
   

Q. Find the sum of the following APs.
(i) 2, 7, 12, …., to 10 terms
(ii) − 37, − 33, − 29 , …, to 12 terms

Q. An AP has 10 terms. If its first and last terms are 5 and 50 respectively, then its sum is

1. 275
2. 325
3. 425