Question

find the sum of terms root 5, 3 root 5, 5 root 5......... 99 root 5 with full explanation​

Answer 1

a = √5

d = a2-a1 = 3√5 - √5 = 2√5

an = 99√5

an = a + (n-1)d

99√5 = √5 + (n-1)*2√5

99√5 - √5 = (n-1)*2√5

98√5 / 2√5 = n-1

49 = n-1                                        [√5 gets cancelled and 98/2 = 49]

n = 49 + 1

n = 50

Sn = n/2 [a + an]

S50 = 50/2 [√5 + 99√5]

       = 25 [100√5]

       = 2500√5

Answer is 2500√5