The first and. the last terms of an A.P. are 17 and 350 respectively. If the difference is 9, how many. terms are there and. what is their sum?

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Solution

$l e t space t h e space n u m b e r space o f space t e r m s space b e space n s o space w e space h a v e space t h e space f o r m u l a e space a subscript n space equals space a space plus space left parenthesis n minus 1 right parenthesis d h e r e space a space equals space 17 space comma space d space 9 space a n d space a subscript n space equals space 350 h e n c e space n space equals fraction numerator space a subscript n space minus a over denominator d end fraction thin space plus 1 space equals space fraction numerator 350 minus 17 over denominator 9 end fraction plus 1 space equals space 37 plus 1 equals 38 h e n c e space t h e space n u m b e r space o f space t e r m s space i s space 38$

Sn = n/2 x (a+l)

Sn = (38/2)(17+350)

Sn = 19x367

Sn = 6973

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