Math, asked by poojarik771, 11 days ago

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 raviapurva1999
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 aanyasg9520
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...

hope it will help you please mark me as brainliest....

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