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If the 10th Term of an A.P. is 21 and the Sum of Its First 10 Terms is 120, Find Its Nth Term. - Mathematics

Sum

If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.

 
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Solution

Let a be the first term and d be the common difference.
We know that, sum of first n terms = Sn = \[\frac{n}{2}\]

and nth term = an = a + (n − 1)d

Now,
S10 =  \[\frac{10}{2}\][2a + (10 − 1)d]

⇒ 120 = 5(2a + 9d)
⇒ 24 = 2a + 9d
⇒ 2a + 9d = 24                    ....(1) 

Also,
a10 = a + (10 − 1)d
⇒ 21 = a + 9d
⇒ 2a + 18= 42                  ....(2)

Subtracting (1) from (2), we get
18d − 9d = 42 − 24
⇒ 9d = 18
⇒ d = 2
⇒ 2a = 24 − 9d             [From (1)]
⇒ 2a = 24 − 9 × 2
⇒ 2a = 24 − 18
⇒ 2a = 6
⇒ a = 3

Also,
an = a + (n − 1)d
    = 
3 + (− 1)2
    = 3 + 2− 2
    = 1 + 2n

Thus, nth term of this A.P. is 1 + 2n.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 29 | Page 52
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