Question

Of the sum of the 3rd and 4th term of an AP is -2 and it's 2nd term is 2. Find the common difference of the AP.​

Answer 1

⇒Logically we know that to find the
`3^(rd)` term we use
`T_(3) =a+2d`

⇒From

`T_(3) =a+(3-1)d\\T_(3)=a+2d`

⇒And the
`4^(th)` is equal
`T_(4) =a+3d` from the same method I used above from the general equation of finding the
`n^(th)` term.

⇒It is said the sum of
`T_(3)` and
`T_(4)` is -2 meaning

`T_(3) +T_(4) =(a+2d)+(a+3d)\\-2=a+2d+a+3d\\-2=a+a+2d+3d\\-2=2a+5d`

⇒It is also said that
`T_(2)` is 2 and we know at this point that

`T_(2) =a+d\\2=a+d`

⇒Then we can use the simultaneous equations technique to find the value of d.

I will use the substitution method by deriving the third equation from the second equation 2=a+d

a=2-d is the
`3^(rd)` equation that I will substitute in the equation

In the place of a it means I will plug in 2-d in the place of a.

`-2=2a+5d\\-2=2(2-d)+5d\\-2=2(2)+2(-d)+5d\\-2=4-2d+5d\\-2-4=3d\\\\3d=-6\\\\`

`(3d)/(3) =(-6)/(3) \\d=-2`

NOTE if you were also asked to find the value of a you can use the equations above to find the value of a which is the first term. the difference represented by letter d is -2.

GOODLUCK!!