Question

@jim_thompson5910 can you help me please

write the explicit general term for the arithmetic sequence where a2 =4 and a6=32 and find the 25 term.

Answer 1

an = a1*(r)^(n-1)

a2 = a1*(r)^(2-1)

a2 = a1*r^1

a2 = a1*r

Answer 2

a2 = a1*r

4 = a1*r

a1 = 4/r

Answer 3

an = a1*(r)^(n-1)

a6 = (4/r)*(r)^(n-1)

a6 = 4*(r)^(6-2)

32 = 4*(r)^(4)

32/4 = r^4

8 = r^4

r^4 = 8

r = (8)^(1/4)

r = 1.68179

a1 = 4/r

a1 = 4/1.68179

a1 = 2.3784182

Answer 4

So after all this, we can say that the sequence is roughly

an = 2.3784182(1.68179)^(n-1)

Answer 5

Your last task is to plug in n = 6 and simplify to get a6

Answer 6

oh wait, i'm thinking of something else

you plug in n = 25 and simplify to find a25

Answer 7

okaii and that will be my final answer

Answer 8

yes

Answer 9

thank you once again :)

Answer 10

yw