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Question

In an A.P, the sum of the first ten terms is 210 and the difference between the first and the last term is 36. Find the first term in the A.P. :
  1. 2
  2. 4
  3. 3
  4. 5

A
2
B
3
C
4
D
5
Solution
Verified by Toppr

Let Sn denote sum of first n terms.
Sn=n2(a+l), where a is the first term and l is the last term.
As given, sum of first ten terms is 210
S10=102(a+l)
210=5(a+l)
42=a+l ............ (1)
And also la=36 ............ (2)
Solving (1) and (2) simultaneously we get
l=39
Substituting l in (2) we get, a=3.
Hence, 3 is the first term.

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