What is the 16th term of the arithmetic sequence 5,12,19,26,...? What is the difference between the 20th and 15th term of an arithmetic sequence with common difference 5? If the 16th term is 47, what

The first term is $a = 5$.
The common difference is $d = 12 - 5 = 7$.

For the 16th term ($n=16$):

The correct option is C) 110.
$\boxed{\text{110}}$

2. What is the difference between the 20th term and 15th term of the arithmetic sequence whose common difference 5?

The common difference is $d = 5$.

The difference between the 20th term and the 15th term is $a_{20} - a_{15}$.

The correct option is C) 25.
$\boxed{\text{25}}$

3. If the 16th term of an arithmetic sequence is 47, what is the sum of the 31st terms?

The 16th term is $a_{16} = a + (16-1)d = a + 15d$.
Given $a_{16} = 47$, so $a + 15d = 47$.

We need to find the sum of the first 31 terms, $S_{31}$.

The correct option is A) 1457.
$\boxed{\text{1457}}$

4. (i) Write the sequence of natural numbers which leaves a remainder 1 on division by 4.

(ii) Is this an arithmetic sequence? Why?

i) Step 1: List the natural numbers that leave a remainder of 1 when divided by 4.
These numbers are $1, 5, 9, 13, 17, \dots$

ii) Step 2: Determine if the sequence is an arithmetic sequence and explain why.
Yes, this is an arithmetic sequence. The difference between consecutive terms is constant:
$5 - 1 = 4$
$9 - 5 = 4$
$13 - 9 = 4$
Since the common difference ($d=4$) is constant, it is an arithmetic sequence.

5. The Sum of terms from 4th to 10th of an arithmetic sequence is 84,

i) What is the 7th term?

ii) What is the sum of 6th term and 8th term.

i) Step 1: Identify the terms and their sum.
The terms are $a_4, a_5, a_6, a_7, a_8, a_9, a_{10}$. There are $10 - 4 + 1 = 7$ terms.
The sum of these 7 terms is 84.

The middle term of these 7 terms is the $\frac{7+1}{2} = 4^{