1. What is the sum of the first six terms of a geometric sequence whose first term is 5 and whose common ratio is 2?*3 points2353103151552. In an arithmetic sequence if a15 = 108 and d=7, find a1.*3 points14101206103. Find dy/dx of 4 sin2y cosx = 2*3 pointsdy/dx=1/2 tan(2y)tanxdy/dx=1/2 tan(y)tanxdy/dx=1/3 tan(2y)tanxdy/dx=-1/2 tan(2y)tanx4. Find y’ when xy+2x² = 4*3 pointsy'=(5+2x-y)/xy'=-(y+5+4x)/xy'=-(y+5+4x)y'=-(y+5+2x)/x5. Find g (x) = 1/√x*3 pointsg' (x)=-1/2 x^(-3/2)g' (x)=1/2 x^(-3/2)g' (x)=-1/2 x^(3/2)g' (x)=1/2 x^(3/2)6. Find the indicated sum for the geometric series. S6 for (-4/5) + 8 + (-80) + 800 + ....*3 pointsS6 = 21,845S6 = 72,000S6 = 72,727.2S6 = -128,840.87.  Solve the system of equations: x-y = -1y =  x² +1*3 points(1,-2) and (0,-1)(1,2) and (0,1)(-1,-2) and (0,-1)(-1,2) and (0,1)8. Solve the system of nonlinear equations:x²+ y² = 10x−3y = −10*3 points(3, -1)(-3, 1)(-1, 3)(1, -3)9.  tan 2π+ sin  2π *3 points012310.  Simplify (cosθ cscθ)/cotθ*3 points-2-101

The first four terms of a sequence are given. Determine whether these terms can be the terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic or geometric, find the next term.(a)    9, −9, 9, −9,   arithmeticgeometric    neither arithmetic or geometricIf the sequence is arithmetic or geometric, find the next term. (If the sequence is neither, enter DNE.) (b)    5, 35, 65, 1,   arithmeticgeometric    neither arithmetic or geometricIf the sequence is arithmetic or geometric, find the next term. (If the sequence is neither, enter DNE.) (c)    2, −1, 12, 2,   arithmeticgeometric    neither arithmetic or geometricIf the sequence is arithmetic or geometric, find the next term. (If the sequence is neither, enter DNE.) (d)    x − 1, x, x + 1, x + 2,   arithmeticgeometric    neither arithmetic or geometricIf the sequence is arithmetic or geometric, find the next term. (If the sequence is neither, enter DNE.)

The third and seventh terms of a geometric sequence are43 and 12 respectively.(a) Find the 10th term.(b) What term is equal to 3072?

In a geometric sequence, the first term is 2 and the fourth term is 250. Find thei. common ratio of this sequence. (3 Marks)ii. 7th term of this sequence.

Determine the common ratio r, the fifth term, and the nth term of the geometric sequence.7, 145, 2825, 56125, . . .r  =  a5  =  an  =

Below is a Geometric sequence with u1 = 5, and the common ratio r5,5√3,53,53√3, .......a) Find the value of r.b) Find the general term un.c) Find which term of the sequence will be 581,d) Show that the sum the infinite terms of the sequence in the form 5√3√3−1.