Question

determine the sum of 22,16,10,...,_80

Answer 1

AP = 22 , 16 , 10 , ........, -80


Here,


First term ( a ) = 22


Common difference ( D ) = 16 - 22 = -6





Tn = -80


a + ( n - 1 ) × D = -80



22 + ( n - 1 ) × -6 = -80



22 - 6n + 6 = -80



-6n + 28 = -80


-6n = -80 - 28


-6n = -108


n = 18.


Number of terms = 18.



Sn = N/2 × [ 2A + ( n - 1 ) × D ]



S18 = 18/2 × [ 2 × 22 + ( 18 - 1 ) × -6 ]




=> 9 × ( 44 - 102 )



=> 9 × -58



=> -522.