(1) 17, 14, 11
(2) 3, 17, 87
(3) n th term = 6 + (n-1)×5
(1) To find the next term, we subtract three from the previous term
Since the first term here is 17, to find the next term we subtract 3 from it
17 - 3 = 14
Now to find the third term, we subtract 3 from the second term
14 - 3 = 11
So the sequence becomes 17, 14, 11,...
(2) To find the next term, we multiply the previous term by 5 and add 2
Since the first term here is 3, we multiply it with 5 and then add 2 to find the second term
3×5 + 2 = 15 + 2 = 17
Now to find the third term, we multiply the second term with 5 and then add 2
17×5 + 2 = 85 + 2 = 87
So the sequence becomes 3, 17, 87,....
(3) Now we have to find the nth term of the given sequence
6 11 16 21
We know the formula for nth term is = a + (n-1)d
For this sequence, a will be 6 as it is the first term
d will be = second term - first term or 11 - 6 = 5
So we put the values in the formula to get
nth term = 6 + (n-1)×5