# What is the next term in the sequence: #sqrtx/3, (2sqrtx)/3, sqrtx,...#?

##### 2 Answers

#### Explanation:

Given:

#sqrt(x)/3, (2sqrt(x))/3, sqrt(x)#

We could also write this as:

#(1sqrt(x))/3, (2sqrt(x))/3, (3sqrt(x))/3#

This is an arithmetic sequence, with common difference

So (if it continues as an arithmetic sequence) the next term is formed by adding the common difference.

#(3sqrt(x))/3 + sqrt(x)/3 = (4sqrt(x))/3#

Next term, I.e. the

#### Explanation:

Difference between

Similarly, difference between

Therefore, the common difference between successive terms

First term

This is an arithmetic progression (A.P) with

Sa_n = a + ((n-1)*d) #

Fourth term