if the 10th term of an is 21 and the sum of its first ten terms is 120 find its 85th term
Answers
Answered by
1
Answer:
171
Step-by-step explanation:
a(10)=21 , S(10) = 120
by formula
S(n) = (n/2)[a+a(n)]
so 120 = (10/2)[a+21]
or 120 = 5[a+21]
or 24 = a+21
or a=3
Now
a(10) = a+9d = 21
or 3+9d = 21
or 9d = 18
or d = 2
Now
a(85) = a+84d
so a(85) = 3+84*2 = 171
Answered by
0
Step-by-step explanation:
a10=21
a+9d=21
where a=first term , d= common difference
a=21-9d
-------(i)
now,
sn=n/2[2a+(n-1)d]
20=10/2[2a+(10-1)d]
120=5[2a+9d]
now,
putting
a=21-9d
[from (i)]
120=5[2(21-9d)+9d]
120/5=42-18d+9d
24=42-9d
-18=-9d
18=9d
d=2
now, putting d=2 in equation (i),
a=21-9d
a=21-18
a=3
now, using an=a+(n-1)d
a85= 3+84(2)
a85= 3+168
a85=171
hence, 85th term of the AP is 171...
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