- The given arithmetic progression is 27, 24, 21, ..., with the first term \( a = 27 \) and the common difference \( d = -3 \).
- The sum of the first \( n \) terms of an A.P. is given by:
\[ S_n = \frac{n}{2} [2a + (n-1)d] \]
- Substituting the known values:
\[ 105 = \frac{n}{2} [2(27) + (n-1)(-3)] \]
Simplifying:
\[ 105 = \frac{n}{2} [54 - 3n + 3] \] \[ 105 = \frac{n}{2} (57 - 3n) \]
Multiplying both sides by 2:
\[ 210 = n(57 - 3n) \]
Solving the quadratic equation:
\[ 210 = 57n - 3n^2 \] \[ 3n^2 - 57n + 210 = 0 \]
Dividing by 3:
\[ n^2 - 19n + 70 = 0 \]
Solving for \( n \):
\[ n = 7 \text{ or } n = 10 \]
- Therefore, \( n = 7 \) gives the sum as 105.
- To find the term that is zero, we use the formula for the \( n \)-th term:
\[ a_n = a + (n-1)d = 27 + (n-1)(-3) = 0 \]
Solving:
\[ 27 + (n-1)(-3) = 0 \] \[ 27 - 3n + 3 = 0 \] \[ 30 = 3n \] \[ n = 10 \]
So, the term is zero at \( n = 10 \).
Select TRUE statements about lymph from the following:
A. Lymph vessels carry lymph through the body and finally open into larger arteries.
B. Lymph contains some amount of plasma, proteins and blood cells.
C. Lymph contains some amount of plasma, proteins and red blood cells.
D. Lymph vessels carry lymph through the body and finally open into larger veins.
The true statements are: