1.

Given a=2 d=8 sn=90 find n and a

Answer»

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First term ( A ) = 2



Common DIFFERENCE ( D ) = 8




Sn = 90


N/2 × [ 2A + ( N - 1 ) × D ] = 90



N/2 × [ 2 × 2 + ( N - 1 ) × 8 ] = 90



N/2 × ( 4 + 8N - 8 ) = 90



N/2 × ( 8N - 4 ) = 90

N/2 × 2 (4N - 2 ) = 90






N ( 4N - 2 ) = 90



4n² - 2n - 90 = 0




2 ( 2n² - n - 45 ) = 0




2n² - n - 45 = 0



2n² - 10n + 9N - 45 = 0


2n ( n - 5 ) + 9 ( n - 5 ) = 0




(n - 5 ) ( 2n + 9 ) = 0



( n -5 ) = 0 or n = -9/2


n = 5 or n = -9/2

Number of terms can't be in fraction.



So,


n = 5.


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