Question

find the first three term of AP first term is -2 and the common difference is -2​

Answer 1

$\large{\underline{\underline{\sf{CORRECT\; QUESTION:}}}}$

Find the next three terms of AP whose first term is -2 and the common difference is -2.

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$\large{\underline{\underline{\sf{ANSWER:}}}}$

Next 3 terms of AP are -4,-6,-8

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$\large{\underline{\underline{\sf{EXPLANATION:}}}}$

Here this is a question from Arithmetic Progression, we have to find the next three terms of AP whose first term and common difference is given. We can find the next term to the 1st term by adding common difference in 1st term. Let's apply this concept to find next 3 terms of the AP.

So let's start!

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GIVEN:

first term, A=-2

Common difference,d=-2

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TO FIND:

Next 3 terms of A.P. which are A2, A3 and A4.

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SOLUTION:

First term is A1=-2   [Given]

$\Large{\underline{\boxed{\sf{For\;2nd\; term}}}}$

2nd term=A1+d

2nd term=-2+(-2)

2nd term=-2-2

2nd term=-4

So A2=-4

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$\Large{\underline{\boxed{\sf{For\;3rd\;term}}}}$

3rd term=A2+d

3rd term=-4+(-2)

3rd term=-4-2

3rd term=-6

So A3=-6

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$\Large{\underline{\boxed{\sf{For\;4th\;term}}}}$

4th term=A3+d

4th term=-6+(-2)

4th term=-6-2

4th term=-8

So A4=-8

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So AP can be formed as follows:

-2,-4,-6,-8

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$\Large{\underline{\underline{\sf{ADDITIONAL\; INFORMATION:}}}}$

To find the nth term have formula:

$\sf{\to An=A+(n-1)d$

To find the sum upto nth term we have formula:

$\sf{\to Sn=\dfrac{n}{2}[2A+(n-1)d]}$

We have another formula to find sum upto nth terms:

$\sf{\to Sn=\dfrac{n}{2}(A+An)}$