Question

if the nth term of an Ap is given by Tn=6n-5 then the 10th term of an Ap is​

Answer 1

Answer:

Step-by-step explanation:

10th term of AP=6(10)-5=60-5=55

Answer 2

Let nth term be the 1st term of the given arithmetic progression.

Given, T{}_{n}n​ = 10 - 6n


∴ T₁ = 10 - 6( 1 )

  T₁ = 10 - 6

  T₁ = 4


We know that the sum of n terms of any arithmetic progression is \dfrac{n}{2} [ T_{1} + T_{n}]2n​[T1​+Tn​]


∴S_{n} = \dfrac{n}{2}[ 4 + 10 - 6n ]Sn​=2n​[4+10−6n]


⇒ S_{n} = \dfrac{n}{2}[ 14 - 6n]Sn​=2n​[14−6n]


⇒ S_{n} = \dfrac{n}{2} \times 2( 7 - 3n )Sn​=2n​×2(7−3n)


⇒ S_{n} = n( 7 - 3n )Sn​=n(7−3n)

⇒ S_{n} = 7n - 3n^2Sn​=7n−3n2



Therefore the sum of n terms of the given AP is 7n - 3n^2.



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