Question

Consider the sequence 3,7,11,15,19,… i) Write down the next two terms of the sequence. ii) Find, in terms n, a formula for the nth term of the sequence. iii) Hence, find the 50th term.

Answer 1

Answer: (i) 23, 37

(ii) 4n - 1

(iii) 199

Step-by-step explanation:

(i)

3, 7, 11, 15, 19, 23, 27

Common difference is four

So the 2 terms after 19 are 23, 27

(ii)

Start with the common difference. It is 4. Now, first term is '3', which is 1 less than 4. The second term is '7' which is 1 less than 8. On observing it is understood that each term of this sequence is 1 less than 4's multiple. 4's multiple can be shown as 4n.

So the given sequence is

4n - 1

Nth term can also be formed from equation:

An = a + (n-1)*d

An = 3 +(n-1)*4

An = 3 + 4n - 4

An = 4n - 1

[An -- n th term, a--1st term=3, d--- common difference=4]

(iii)

50th term=== 4n-1...... substitute n=50

4×50 - 1 = 200-1 = 199