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

Answer:

sorry i cant find the answer

Answer 2

Answer:

The fifth term in the progression is -4.

Step-by-step explanation:

In an arithmetic progression, there are 6 terms and their sum is 3.

we know that

$S_{n}=\frac{n}{2}(2a+(n-1)d)$...........................(1)

As n=6 and $S_{n}=3$

put $S_{n}$ and n in (1) we get

$S_{6}=\frac{6}{2}(2a+5d)$

$1=2a+5d$.....................................(2)

The first term is 4 times the third term

$a_{1} =4\times a_{3}$

$a=4(a+2d)$

after solving we get

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

Now we have two equation (2) and (3)

solve by elimination method we get

a=8 and d=-3

so the fifth term is

$a_{5}=a+4d$

               =$8+4\times(-3)$

               =-4

The fifth term in the progression is -4.