Question

how many terms are in ap whose first and eight yerms are -16 and -2 respectively and the sum of terms is 18

Answer 1

first term(a)=-16
eighth term=a+7d
-2=-16+7d
16-2=7d
14=7d
d=14/7
d=2
now common difference=2
sum of terms = 18
S = n/2[2a+(n-1)d]
18 =n/2[2×-16+(n-1)2]
18×2=n[-32+(n-1)2]
36 = -32n +2nsquare-2n(÷2)
18= -16n+nsq. -n
0=nsq. -17n-18
0= nsq. -18n+n-18
0=n(n -18)+1(n-18)
0=(n-18)(n+1)
if n-18=0
n=18
if n+1=0
n=-1 which is not possible
therefore total terms of the ap are 18