Given sequence :2;6;10;14;18;.....
What will be value of 89^th term, for the odd positions of sequences above.
To find the value of the 89th term for the odd positions in the given sequence, we need to determine the pattern of the sequence.
Looking at the sequence, we can observe that each term is obtained by adding 4 to the previous term.
Let's denote the first term as a and the common difference as d.
a(1) = 2 (first term)
d = 4 (common difference)
The nth term formula for an arithmetic sequence is:
a(n) = a(1) + (n-1)d
Since we are looking for the odd positions, we can use the formula:
a(n) = a(1) + (2n-2)d
Plugging in the values:
a(89) = 2 + (2*89-2)*4
= 2 + (178-2)*4
= 2 + 176*4
= 2 + 704
= 706
Therefore, the value of the 89th term for the odd positions in the given sequence is 706.