Question

Find the sum to n terms of the AP . whose Kth term is 5k+1

Answer 1

Answer:

3n ( n + 1 )

Step-by-step explanation:

Given----> Kth term of AP is ( 5k + 1 ).

To find---> Sum of n terms of given AP.

Solution---> ATQ,

Kth term of AP = ( 5k + 1 )

aₖ = ( 5k + 1 )

If we put K = 1 , 2, 3, ......etc., we get first , second , third terms respectively.

Putting k = 1 , in it,

a₁ = 5 ( 1 ) + 1

= 5 + 1 = 6

Putting k = 2 , in it,

a₂ = 5 ( 2 ) + 1

= 10 + 1

= 11

First term = 6 , Common difference = 11 - 5 = 6

Now , Sum of n terms of AP ,

Sₙ = n / 2 { 2a + ( n - 1 ) d }

= n / 2 { 2 ( 6 ) + ( n - 1 ) 6 }

= n / 2 ( 12 + 6n - 6 )

= n / 2 ( 6n + 6 )

= 6 n ( n + 1 ) / 2

= 3 n ( n + 1 )

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Answer 2

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$\huge\underline{\underline{\texttt{\purple{3n(n+1)}}}}$

#answerwithquality #bal