Question

If the sum of first 7 terms of an AP. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.

Answer 1

See the attachment here


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Answer 2

Solution :

Let a be the first term and d be the

common difference of given A P .

i) Sum of first 7 terms = 49

=> (7/2)[ 2a + (7-1)d ] = 49

=> (7/2)[2a + 6d] = 49

=> 7( a + 3d ) = 49

=> a + 3d = 7 -----( 1 )

ii ) Sum of first 17 terms = 289

=>(17/2) [ 2a + (17-1)d ] = 289

=> (17/2)[ 2a + 16d ] = 289

=> (17/2)[2(a+8d)] = 289

=> 17(a+8d) = 289

=> a + 8d = 17 ------( 2 )

Subtracting ( 1 ) from ( 2 ) , we get

=> 5d = 10

=> d = 2

Substitute d = 2 in equation ( 1 ),

we get

a + 3×2 = 7

=> a + 6 = 7

=> a = 7 - 6

=> a = 1

Now ,

Sum of n terms = Sn

= n/2[ 2×1 + ( n - 1 )2 ]

= (n/2) [ 2 + 2n - 2 ]

= (n/2) × 2n

= n²

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