First term ,a=4 , common difference =4-7=-3, n =50
sum of first 50terms= (50/2)[2×4+(50-1)(-3)]
=25×[8+49]×-3
=25×57×-3
=25× -171
= -42925
derivation of the formula for the sum of n terms
Progression, S
S=a1+a2+a3+a4+...+an
S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d] → Equation (1)
S=an+an−1+an−2+an−3+...+a1
S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n−1)d] → Equation (2)
Add Equations (1) and (2)
2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)
2S=n(a1+an)
S=n/2(a1+an)
Substitute an = a1 + (n - 1)d to the above equation, we have
S=n/2{a1+[a1+(n−1)d]}
S=n/2[2a1+(n−1)d]
Answer: See explanation
Step-by-step explanation:
7x - 2(x + 3y) + 3y
= 7x - 2x - 6y + 3y
= 5x - 3y
Will got 5x + 9y because he didn't multiply the values in the bracket by the minus sign outside the bracket. He multiplied the values by +2 rather than -2. This resulted in the wrong answer that he got.
The probability of having a boy: 1/2
1/2(1/2)(1/2)=1/8
The probability of a family having three boys is 1/8.
Hope this helps!
Answer:
n = 0, n =2
Step-by-step explanation:
Given
(n + 1) + 3(n - 1) = 2(n - 1)(n + 1) ← distribute parenthesis on both sides
n + 1 + 3n - 3 = 2(n² - 1), that is
4n - 2 = 2n² - 2 ( subtract 4n - 2 from both sides )
0 = 2n² - 4n ← factor out 2n from each term )
0 = 2n(n - 2)
Equate each factor to zero and solve for n
2n = 0 ⇒ n = 0
n - 2 = 0 ⇒ n = 2
Answer:
mhhh
Step-by-step explanation:
