In an arithmetic sequence, a3=15 and a8=0. What is the value of a5?

a3=15 , n=3

a8=0, n=8

a5 = ?

an = a1+ (n-1)d

a3 = a1 + (3-1) d

a3=a1+2d

and a8 = a1 + (8-1 )d

a8= a1+ 7d

15 = a1 + 2 d1

0= a1 +7 d2

substacting eq 2 from eq 1

15= - 5d

- 5d = 15

divide by - 5

d = -3

putting the value of d in eq 1

15 = a1 + 7 (-3)

15 = a1 -21

adding 21 on both sides

a1-21+21= 15+21

a1 = 36

a5 = ?, n=5, d= -3, a1=36

a5 = 36 + (5-1) (-3)

= 36+(4)(-3)

= 36-12

= 24

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