Question

An arithmetic series is such that the ninth term is zero and the sum of the
first 25 terms is 50. The first term of the series is:​

Answer 1

Answer:

First term = -4

Step-by-step explanation:

Ninth term T9 = a+8d (where a is the first term and d is the common difference )

a+8d = 0

Therefore, a = -8d

General formula for sum of n terms in an AP is:

Sn = (n/2)(2a+(n-1)d)

Substituting values of n as 25, a as -8d we get,

S25 = (25/2)(2*(-8d)+(25-1)d)

We know sum of 25 digits = 50, therefore S25 = 50

50 = (25/2)(-16d+24d)

50 = (25*8d)/2

50 = 100d

Therefore d = 1/2

Substituting the value of d in a = -8d,

We get a = -4