Solveeit Logo
Login

Question

Question: If the first second and last term of an A.P. are a, b, c then the number of terms will be-...

If the first second and last term of an A.P. are a, b, c then the

number of terms will be-

A

a+b+c2\frac{a + b + c}{2}

B

b+c−2a2\frac{b + c - 2a}{2}

C

(b+c−2a)(b−a)\frac{(b + c - 2a)}{(b - a)}

D

None

Answer

(b+c−2a)(b−a)\frac{(b + c - 2a)}{(b - a)}

Explanation

Solution

First term = a, common difference d = b –a

Tn = c = a + (n –1) d

c – a = (n –1) (b –a)

n –1 = c−ab−a\frac{c - a}{b - a}

n = c−ab−a\frac{c - a}{b - a}+ 1=c−a+b−ab−a\frac{c - a + b - a}{b - a}= b+c−2ab−a\frac{b + c - 2a}{b - a}