If A1 and A2 are known to be equal difference sequence and A1 = 10, their arithmetic mean is 53.5, then A13 is equal to I figured out 46, but every option was 46 a1 a2 a3 …… A30 is the arithmetic mean of arithmetic difference sequence
a(n)=10+(n-1)d,
a(2)=10+d,
53.5 = [a(1)+a(2)]/2 = [20+d]/2,d= 107 - 20 = 87.
a(n)=10+87(n-1).
a(13)=10+87*12=1054.
In the expansion of (x ^ 3 + 1 / x ^ 2) ^ n, only the sixth term has the largest coefficient, then n =?
With binomial theorem solution, 3Q!
1
eleven
one hundred and twenty-one
one thousand three hundred and thirty-one
1,5,10,10,5,1
1,6,15,20,15,6,1
From Yang Hui's triangle, we can see that the coefficient of (a + b) ^ n expansion is the largest ([n / 2] + 1). (when n is an odd number, there is also a ([n / 2] + 2) term which is also large. [x] is the integral part of X.)
When [n / 2] + 1 = 6, n = 10 or 11
If the maximum coefficient has only one term, then n = 10
If (x ^ 2 - (1 / x)) ^ n expansion contains the sixth term, find the coefficient containing the fourth term
T6=C(n,5)*(x²)^(n-5)*(-1/x)^5
The exponent of X is 2 (N-5) - 5 = 2n-15 = 1
∴ n=8
The general term of (x ^ 2 - (1 / x)) ^ n expansion is t (R + 1)
∴ T(r+1)=C(8,r)*(x²)^(8-r)*(-1/x)^r
The exponent of X is 2 (8-r) - r = 16-3r = 4
∴ r=4
The coefficient of T5 is C (8,4) * - 1) ^ 4 = C (8,4) = 8 * 7 * 6 * 5 / (1 * 2 * 3 * 4) = 70
The coefficient of x ^ 4 is 70