The first, second and the middle terms of an
a.P are a, b, c respectively. Then their sum is equal to:
Answers
Answer:
Sum = 3b
Sum = (number of terms) * middle Term
Step-by-step explanation:
The first, second and the middle terms of an a.P are a, b, c respectively. Then their sum is equal to:
Sum = a + b + c
d = b - a
d = c - b
=> b -a = c - b
=> 2b = c + a
putting value of a + c = 2b in Sum
Sum = 2b + b
=> Sum = 3b
Sum = 3 times the middle terms
=> Sum = (number of terms) * middle Term
Answer: ((2c(c-a))/(b-a)) + c
Step-by-step explanation: Consider the A.P.- a1,a2,a3,a4....,an
Given: a1=a, a2=b
Difference, d=a2-a1=b-a
Middle Term of the A.P.=a1 + ((n+1)/2)d = a+((n+1)/2)(b-a) = c
=>n=((2(c-a))/(b-a)) + 1
Sum of A.P.=(n/2)(a1+an)
= (n/2)(2a1+(n-1)d)
= {(((2(c-a))/(b-a)) + 1)/2}[2a+(((2(c-a))/(b-a)) + 1-1)(b-a)]
= {((2(c-a))/(b-a))+1}[a+c-a]
= (((2c(c-a))/(b-a)) + c