Basic Adding Patterns in an AP

Q.

If t(n) represents the $n^{th}$ term of an AP, then which of the following is always true?

1. t(1) + t(20) = t(19) + t(2)

2. t(2) + t(18) = t(4) + t(16)

3. t(1) + t(20) = t(21)

4. None of the above

Q. The sum of n, 2n, 3n terms of an AP are $S_1,S_2,S_3$ respectively. Prove that $S_3=3(S_2-S_1)$

Q.

Extending the same logic you’ve seen in the video so far, find out the sum of the first 10 natural numbers.
(You can use $S_{10}=1+2+3+\dots +10$ and proceed)

1. $\frac{(10\times 11)}{2}$

2. None of these

3. $10\times 11$

4. $\frac{(10\times 2)}{11}$

Q.

Find the value of
9 $\times$ 9 – 30 $÷$ 3 + 5 – 6 + 7 – 2 + 9 $\times$ 9

1. 324

2. 154

3. 156

4. 248