Question

3,7,11,... is an arithmetic sequence.

a) Write the common difference of this arithmetic sequence

b) What is the 16th term of this arithmetic sequence?​

Answer 1

Answer:

The common difference is the value between each successive number in an arithmetic sequence. Therefore, the formula to find the common difference of an arithmetic sequence is: d = a(n) - a(n - 1), where a(n) is the last term in the sequence, and a(n - 1) is the previous term in the sequence.

Step-by-step explanation:

Hope it helps

Answer 2

Answer:

a) Common difference of this arithmetic sequence is = 4

b) The 16th term of this arithmetic sequence is = 63

Step-by-step explanation:

• A sequence of numbers where the difference between the consecutive terms is a constant is called an arithmetic sequence or arithmetic progression.

                           $a_{n} , a_{n+1}, a_{n+2} ,...$

Where aₙ₊₁ - aₙ = aₙ₊₂ - aₙ₊₁ and so on.

• The difference between the two consecutive terms in an arithmetic sequence is always a constant and is known as common difference 'd'.

                           $d=a_{n+1}-a_{n}$

• The general term of an arithmetic sequence with initial term a₁ and common difference d is given by

                          $a_{n} = a_{1} +(n-1)d$

Step 1:

The given arithmetic sequence is as follows,

3, 7, 11,.........

The difference between two consecutive terms,

7- 3 = 4 and 11 - 7 = 4

∴ The common difference, d = 4

Step 2:

The 16th term of the sequence can be found as,

a₁₆ = a₁ + 15d

We have a₁ = 3 and we have found d = 4

∴ a₁₆ = 3 + 15×4

a₁₆ = 3 + 60

a₁₆ = 63

∴ The 16th term, a₁₆ = 63