Question

if the first term of an AP is equal to twice the second term of the same AP then find the third term.​

Answer 1

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Answer 2

Answer:

The third term of the AP is 0.

Step-by-step explanation:

The nth term of an AP is:

$T_{n}=a+(n-1)d$

Here,

a = first term

d = common difference

It is provided that:

$a=2T_{2}$

Solve the above equation for a as follows:

$a=2T_{2}\\a=2[a+(n-1)d]\\a=2[a+(2-1)d]\\a=2a+2d\\a=-2d$

Compute the third term as follows:

$T_{3}=a+(3-1)d=a+2d=-2d+2d=0$

Thus, the third term of the AP is 0.