The fifth term of an arithmetic sequence is equal to 6 and the sum of the first 12 terms is 45. Find the first term and the common difference.
Arithmatic term n, Un= U1+(n-1)d. Where U1 is the first term of the sequence and d is the common difference. U5=U1+4d=6. U1=6-4d. Sum of arithmatic terms up to term n, Sn=n/2(2U1+(n-1)d). S12=12/2(2(6-4d)+(12-1)d)=45. 6(12-8d+11d)=45. 12+3d=45/6. 3d=7,5-12=-4,5. d=-4.5/3=-1,5. U1=6-4*(-1,5)=6+6=12
JS
Related Maths IB answers
All answers ▸Solve the integral int(sin^2(x))dx
Given that w=x * e^-w use implicit differentiation to show that dw/dx=1/(e^w + x)
Given 1/2 + 1 + 2 + 2^2 + ... + 2^10 = a*2^b + c, find the values of a,b,c.
A team of four is chosen from six married couples. If a husband and wife cannot both be on the team, in how many ways can the team be formed?