Question

Find the sum of AP in (-5)+(-8)+(-11)+.....+(-230)​

Answer 1

Answer:

-8930

Step-by-step explanation:

(-5) + (-8) + (-11) +.....+(-230)

First term = a = (-5)

Common difference = d = (-8) - (-5) = (-8) + 5 = (-3)

nth term = aₙ =  (-230)

aₙ = a + (n-1) d

=> -230 = (-5) + (n-1)(-3)

=> -230 = -5 - 3n + 3

=> -230 = -2 - 3n

=> 3n = 230 - 2 = 228

=> n = 228 ÷ 3 = 76

Sum of AP = $\frac{n}{2} [2a + (n-1)d]$

                 = $\frac{76}{2} [2(-5) + (76-1) (-3)]$

                 = 38[(-10) + (75)(-3)]

                 = 38[-10 - 225]

                 = 38 x (-235)

                 = -8930

Hence, the sum of the given AP is -8930.     [Answer]