Question

find second and third term of an arithmetic progression whose first term is -2 and common difference is -2​

Answer 1

Given:-

• First term of AP, a₁ = -2
• Common difference, d = -2

To Find:-

• Second term of AP, a₂ ?
• And third term of AP, a₃ ?

Solution :-

It's given that first term and common difference is equal to -2 and -2. And for second term of AP, number of terms(ₙ) will be equal to 2.

So as we know that:-

⇒ aₙ = a + (n-1)d

⇒ a₂ = a + (n-1)d

⇒ a₂ = -2 + (2-1)-2

⇒ a₂ = -2 -2

⇒ a₂ = -4

Therefore, the second term(a₂) of AP is -4.

Now, for third term, number of terms(ₙ) will be equal to 3 And common difference and first term will remain same.

⇒ a₃ = a + 2d

⇒ a₃ = -2 + 2(-2)

⇒ a₃ = -2 - 4

⇒ a₃ = -6

Therefore, the third term(a₃) of AP is -6.

• NOTE:- here we could use the aₙ=a+(n-1)d formula too, for finding the third term.

Answer 2

AnswEr-:

• $\underline{\pink{\boxed {\mathrm {\bf{ a_{2} \: or\:Second\:term\:of\:A.P \:= -4}}}}}$

• $\underline{\pink{\boxed {\mathrm {\bf{ a_{3} \: or\:Third\:term\:of\:A.P \:= -6}}}}}$

Explanation-:

$\mathrm { Given -:}$

• First Term of A.P or $\sf{a_{1}}$ or a is -2 .
• Common Difference or D is -2

$\mathrm { To\:Find -:}$

• $\sf{a_{2}}$ or Second term of A.P.
• $\sf{a_{3}}$ or Third term of A.P .

$\dag{\mathrm { Solution \:of\:Question-:}}$

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As , We know that,

• $\underline{\red{\boxed {\dag{\mathrm{a_{n} = a +(n-1) d }}}}}$

• Here ,
• First Term of A.P or $\sf{a_{1}}$ or a is -2 .
• -2 .Common Difference or D is -2
• $\sf{a_{n} }$ or Number of term -: 2 nd Term

Now , By Putting known Values in Formula-:

• $\longrightarrow {\mathrm {\bf{ a_{2} = (-2)+(2-1)(-2)}}}$

• $\longrightarrow {\mathrm {\bf{ a_{2} = (-2)+1 (-2)}}}$

• $\longrightarrow {\mathrm {\bf{ a_{2} = -2-2}}}$

• $\underline{\pink{\boxed {\mathrm {\bf{ a_{2} = -4}}}}}$

Therefore-:

• $\underline{\pink{\boxed {\mathrm {\bf{ a_{2} \: or\:Second\:term\:of\:A.P \:= -4}}}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline {\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}\:$

Now , As , We know that,

• $\underline{\red{\boxed {\dag{\mathrm{a_{n} = a +(n-1) d }}}}}$

• Here ,
• First Term of A.P or $\sf{a_{1}}$ or a is -2 .
• Common Difference or D is -2
• $\sf{a_{n} }$ or Number of term -: 3 rd Term

Now , By Putting known Values in Formula-:

• $\longrightarrow {\mathrm {\bf{ a_{3} = (-2)+(3-1)(-2)}}}$

• $\longrightarrow {\mathrm {\bf{ a_{3} = (-2)+2 (-2)}}}$

• $\longrightarrow {\mathrm {\bf{ a_{3} = -2-4}}}$

• $\underline{\pink{\boxed {\mathrm {\bf{ a_{2} = -6}}}}}$

Therefore-:

• $\underline{\pink{\boxed {\mathrm {\bf{ a_{3} \: or\:Third\:term\:of\:A.P \:= -6}}}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline {\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}\:$

Hence ,

• $\underline{\pink{\boxed {\mathrm {\bf{ a_{2} \: or\:Second\:term\:of\:A.P \:= -4}}}}}$

• $\underline{\pink{\boxed {\mathrm {\bf{ a_{3} \: or\:Third\:term\:of\:A.P \:= -6}}}}}$

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