Using 1994 as origin, obtain a straight-line trend by the method of least square. Also find the value for year 1997.

Here, $n = 7$.
$\sum Y = 1120$
$\sum X = -7$
$\sum XY = -928$
$\sum X^2 = 35$

1. $1120 = 7a + (-7)b \implies 1120 = 7a - 7b$
2. $-928 = (-7)a + 35b \implies -928 = -7a + 35b$

Add equation (1) and equation (2):
$(1120) + (-928) = (7a - 7b) + (-7a + 35b)$
$192 = 28b$
$b = \frac{192}{28} = \frac{48}{7} \approx 6.857$

Substitute the value of $b$ into equation (1):
$1120 = 7a - 7 \left(\frac{48}{7}\right)$
$1120 = 7a - 48$
$1120 + 48 = 7a$
$1168 = 7a$
$a = \frac{1168}{7} \approx 166.857$

$Y_c = a + bX$
$Y_c = 166.857 + 6.857X$

For the year 1997, $X = 1997 - 1994 = 3$.
Substitute $X=3$ into the trend equation:
$Y_c = 166.857 + 6.857(3)$
$Y_c = 166.857 + 20.571$
$Y_c = 187.428$

The straight-line trend equation is $\boxed{Y_c = 166.857 + 6.857X}$.
The trend value for the year 1997 is $\boxed{187.428}$.