Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

7. Given an arithmetic sequence, find a26if a4 = 71 and a32 = 1. 8. Given a geometric sequence, find az ifa1 = 729 and a2 = – 243.

Sagot :

Arithmetic sequence

a= 26

a4 = 71

a32 = 1.

an = a1 + (n-1)d

a4 = a1 + (3)*d

71 = a1 + (3)*d (I)

a32 = a1 + (31)*d

1 = a1 + 31 d (II)

to find a1 and d we subtract (II)- (I)

1 = a1 + 31 d (II)

-( 71 = a1 + (3)*d) (I)

________________

-70 = 0 28 d

-70 = 28 d

d= -70/ 28

d= -5/2

Replacing d in (I)

71 = a1 - (3)(5/2)

a1= 71 + (3)(5/2)

a1= 78.5

The arithmetic sequence is

an = a1 + (n-1)d

an = 78.5 + 2.5 (n-1)

Verifying

a4 = 78.5 - 2.5 (3) = 78.5 -7.5= 71

a32 = 78.5 +2.5 (31) =78.5 -77.5 = 1

a26 = 78.5 + 2.5 (25) = 78.5 - 62.5 = 16

Give me some minutes

______________________

Answer

a26 = 16

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.