Answer: S₁₉ = 855
Step-by-step explanation:
T₄ = a + ( n - 1 )d = 5 , from the statement above , but n = 4
a + 3d = 5 -------------------------1
S₆ = ⁿ/₂[(2a + ( n - 1 )d] = 10, where n = 6
= ⁶/₂( 2a + 5d ) = 10
= 3( 2a + 5d ) = 10
= 6a + 15d = 10 -----------------2
Now solve the two equation together simultaneously to get the values of a and d
a + 3d = 5
6a + 15d = 10
from 1,
a = 5 - 3d -------------------------------3
Now put (3) in equation 2 and open the brackets
6( 5 - 3d ) + 15d = 10
30 - 18d + 15d = 10
30 - 3d = 10
3d = 30 - 10
3d = 20
d = ²⁰/₃.
Now substitute for d to get a in equation 3
a = 5 - 3( ²⁰/₃)
a = 5 - 3 ₓ ²⁰/₃
= 5 - 20
a = -15.
Now to find the sum of the first 19 terms,
we use the formula
S₁₉ = ⁿ/₂( 2a + ( n - 1 )d )
= ¹⁹/₂( 2 x -15 + 18 x ²⁰/₃ )
= ¹⁹/₂( -30 + 6 x 20 )
= ¹⁹/₂( -30 + 120 )
= ¹⁹/₂( 90 )
= ¹⁹/₂ x 90
= 19 x 45
= 855
Therefore,
S₁₉ = 855
Answer:
3+11x+11y-4x^2-8xy-4y^2
Step-by-step explanation:
Using the distributive property, we get 3+11x+11y-4x^2-8xy-4y^2
The area of a trapezium is
A = (a<span>+</span><span>b)*h</span><span>/2
24 + 18 = 46 * 5 = 230 / 2 = 115</span>
Answer:
7.2/3 ± (isqrt2)/3
8.2±i
9.-0.4±0.2
10.1/3±1/3sqrt19
Step-by-step explanation:
7. a =3, b=-4, c=2
plugging in to the quadratic formula
(2 ± isqrt2)/3
8.a=1,b=-4.c=5
plugging in to the quadratic formula
2±i
9.a=5,b=4,c=2
plugging in to the quadratic formula
-0.4±0.2
10.a=-3,b=2,c=6
plugging in to the quadratic formula
1/3±1/3sqrt19