**Solution: Sum of n terms of Series 1.4, 3.7, 5.10**

To find the sum of n terms of the given series, we need to first determine the pattern followed by the series.

**Pattern of the Series:**

Looking at the given series, we can observe that each term is obtained by multiplying the corresponding term number with a constant and adding another constant to it.

For example,

- The first term (term number = 1) is obtained by multiplying 1 with 1.4 and adding 0.
- The second term (term number = 2) is obtained by multiplying 2 with 1.4 and adding 2.3.
- The third term (term number = 3) is obtained by multiplying 3 with 1.4 and adding 3.6.

Thus, the pattern of the series can be expressed as:

Term n = n x 1.4 + (n-1) x (n-1) x 0.3

**Sum of n terms of the Series:**

To find the sum of n terms of the series, we need to add up all the terms from the first term to the nth term.

Let Sn be the sum of n terms of the series. Then,

Sn = 1.4 + (1 x 1.4 + 2 x 3) + (3 x 1.4 + 4 x 3.3) + ... + [(n-1) x 1.4 + n x (n-1) x 0.3]

Simplifying this expression, we get:

Sn = 1.4n + 0.3 [1^2 + 2^2 + 3^2 + ... + (n-1)^2]

The sum of squares of first n natural numbers can be expressed as:

1^2 + 2^2 + 3^2 + ... + (n-1)^2 = n(n-1)(2n-1)/6

Substituting this value in the above expression for Sn, we get:

Sn = 1.4n + 0.3n(n-1)(2n-1)/6

Simplifying further, we get:

Sn = n/6 [7n + 3(n-1)(2n-1)]

Thus, the sum of n terms of the given series is n/6 [7n + 3(n-1)(2n-1)].