Question

Please answer this question
See the attachment

Answer 1

Answer:

r=-2 and a=2.25

Step-by-step explanation:

Given:

First term= a, common ratio= r  (terms alternate in sign), S₄=5S₂

To find:

a) r=?

b) a₅=36, a=?

============

• Sₙ=a(rⁿ-1)/(r-1) - formula for sum of first n terms

• S₄=a(r⁴-1)/(r-1)
• S₂=a(r²-1)/(r-1)
• S₄/S₂=a(r⁴-1)/(r-1): a(r²-1)/(r-1)= (r⁴-1)/(r²-1)=(r²+1)(r²-1)/(r²-1)=r²+1
• And we have S₄=5S₂ => S₄/S₂=5
• r²+1=5
• r²=4
• r=±2

Since terms are alternating in sign, the common ratio is r= -2

Now,

• a₅=a*r⁴=a*(-2)⁴=a*16
• 16a=36
• a=36/16
• a=9/4 or 2.25

Answer:

r=-2 and a=2.25

Answer 2

Answer:

your answer is.......

r=-2

and

a is 2.25

hope it helps you Mate