Question

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The sum of first 10 terms of an Arithmetic Progression is 55 and the sum of first 9 terms
of the same arithmetic progression is 45. Then its 10th term is.
A) 9
B)55
C) 12
D)10​

Answer 1

Answer:

10    (option D)

Step-by-step explanation:

      Given, S₉ = 45, S₁₀ = 55

⇒ S₁₀ = 1st term + 2nd term + ... 10th term

⇒ S₁₀ = sum of first 9 term + 10th term

⇒ S₁₀ = S₉ + T₁₀

⇒ 55 = 45 = T₁₀

⇒ 10 = T₁₀

 Hence the 10th term is 10

     Technique 2:

S₁₀ = (10/2)[2a + 9d] = 10a + 45d = 55

S₉ = (9/2)[2a + 8d] = 9a + 36d  = 45  

 Solving these equations, we get

a = 1, and d = 1

 Hence 10th term = a + 9d

             = 1 + 9(1) = 10

Answer 2

Given :-

The sum of first 10 terms of an Arithmetic Progression is 55 and the sum of first 9 terms  of the same arithmetic progression is 45

To Find :-

10th term

Solution :-

We know that

$\sf a_n = a+(n-1)d$

$\sf Sum\;of\;10 \;terms = 55$

$\sf Sum\;of\;9\;terms=45$

$\sf 10^{th}\;term=Sum\;of\;10\;term-Sum\;of\;9\;term$

$\sf 10^{th}\;term= 55 - 45$

$\sf 10^{th}\;term=10$