Question

Find the 20th term of the sequence 2, 8, 18, 32, ... ​

Answer 1

20th term of sequence is 800

Solution:

Given sequence is 2, 8, 18, 32

To find: 20th term of sequence

Let us first find the pattern followed by sequence

$2 \times 1 \times 1 = 2\\\\2 \times 2 \times 2 = 8\\\\2 \times 3 \times 3 = 18\\\\2 \times 4 \times 4 = 32$

So the next term is found by multiplying 2 with the square of location of term

For nth term, we can represent by

$a_n = 2n^2$

Where, n = 1, 2, 3, .........

To find 20th term

n = 20

$a_{20} = 2(20)^2 = 2 \times 400 = 800$

Thus 20th term of sequence is 800