Question

In an arithmetic progression there are 6 terms and their sum is 3. the first term is 4 times the third term. the fifth term in the progression is?

Answer 1

hey buddy here is your answer BY UDIT

let the first term be
a
and common difference be
d

then given series is

a , a+d, a+2d, a+3d ,a+4d, a+5d

given sum of AP is 3

so .

a+a+d+a+2d+a+3d+a+4d+a+5d =3

6a+15d =3 ............ (1)

and

given

the first term is 4 times the third term

a=4(a+2d)

3a+8d=0 ............. (2)

solving 1 and 2 we get

d=-3 and a =8

so the fifth term is a + 4d

=8+4×(-1) = 4


thanks

Answer 2

no. of terms = 6
sum to 6 terms = 3
we have
a = 4third term
third term = a + 2d
a = 4(a+2d)
formula for sum to n terms
3 = 3 ( -8/3 d + 5d )
3 = 3 (7/3 d )
3 = 7d
d = 7/3
now a = -8/3 d
= -56/9
fifth term = -56/3 + 4 × 7/3
= -56/3 + 28/3
= -28/3