Question

sn=n/2[2a+(n-1) d, sn=72, a=17, d=-2 find n​

Answer 1

Step-by-step explanation:

a

n

=a+(n−1)d

4=a+(n−1)2

4=a+2n−2

6=a+2n

∴a=6−2n...(1)

S

n

=

2

n

[2a+(n−1)d]

−14=

2

n

[2(6−2n)+(n−1)2]

−28=n[12−4n+2n−2]

−28=12n−2n

2

−2n

−28=10n−2n

2

−14=5n−n

2

Solving the above equation, we get,

(n−7)(n+2)=0

n=7,−2

∴n=7

a=6−2n From (1)

a=6−2(7)=−8

Answer 2

Step-by-step explanation:

sn=72

n/2[2×17+(n-1)-2]=72

n[34-2n+2]=144

36n-2n²=144

rearranging

2n²-36n+144=0

(n-12)(n-6)=0

n=6,12