Answer:
0 , -5 ,-10 ,-15
Step-by-step explanation:
i hope it's helpful
[tex] \qquad \:\boxed{ \bf{ \:5, \: 0, \: - 5, \: - 10 \: \: }} \\ \\ [/tex]
Given that,
First term of an AP series, a = 5
Common difference of an AP, d = - 5
So,
[tex]\sf\implies a_1 = 5 \\ \\ [/tex]
Consider,
[tex]\sf \: a_2 \\ \\ [/tex]
[tex]\sf \: = \: a_1 + d \\ \\ [/tex]
[tex]\sf \: = \: 5 - 5 \\ \\ [/tex]
[tex]\sf \: = \: 0 \\ \\ [/tex]
[tex]\sf\implies a_2 = 0 \\ \\ [/tex]
Now, Consider
[tex]\sf \: a_3 \\ \\ [/tex]
[tex]\sf \: = \: a_2 + d \\ \\ [/tex]
[tex]\sf \: = \: 0 - 5 \\ \\ [/tex]
[tex]\sf \: = \: - 5 \\ \\ [/tex]
[tex]\sf\implies a_3 = - 5 \\ \\ [/tex]
[tex]\sf \: a_4 \\ \\ [/tex]
[tex]\sf \: = \: a_3 + d \\ \\ [/tex]
[tex]\sf \: = \: - 5 - 5 \\ \\ [/tex]
[tex]\sf \: = \: - 10 \\ \\ [/tex]
[tex]\sf\implies a_4 = - 10 \\ \\ [/tex]
So, first four terms of an AP series whose first term, a = 5 and common difference, d = - 5 is
[tex]\boxed{ \sf{ \:5, \: 0, \: - 5, \: - 10 \: \: }} \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
↝ nᵗʰ term of an arithmetic progression is,
[tex]\begin{gathered}\bigstar\:\:{\underline{{\boxed{\bf{{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}[/tex]
↝ Sum of n terms of an arithmetic progression is,
[tex]\begin{gathered}\bigstar\:\:{\underline{{\boxed{\bf{{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}[/tex]
Wʜᴇʀᴇ,
Sₙ is the sum of n terms of AP.
a is the first term of the progression.
n is the no. of terms.
d is the common difference.
aₙ is the nᵗʰ term.
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Answers & Comments
Answer:
0 , -5 ,-10 ,-15
Step-by-step explanation:
i hope it's helpful
Verified answer
Answer:
[tex] \qquad \:\boxed{ \bf{ \:5, \: 0, \: - 5, \: - 10 \: \: }} \\ \\ [/tex]
Step-by-step explanation:
Given that,
First term of an AP series, a = 5
Common difference of an AP, d = - 5
So,
[tex]\sf\implies a_1 = 5 \\ \\ [/tex]
Consider,
[tex]\sf \: a_2 \\ \\ [/tex]
[tex]\sf \: = \: a_1 + d \\ \\ [/tex]
[tex]\sf \: = \: 5 - 5 \\ \\ [/tex]
[tex]\sf \: = \: 0 \\ \\ [/tex]
[tex]\sf\implies a_2 = 0 \\ \\ [/tex]
Now, Consider
[tex]\sf \: a_3 \\ \\ [/tex]
[tex]\sf \: = \: a_2 + d \\ \\ [/tex]
[tex]\sf \: = \: 0 - 5 \\ \\ [/tex]
[tex]\sf \: = \: - 5 \\ \\ [/tex]
[tex]\sf\implies a_3 = - 5 \\ \\ [/tex]
Now, Consider
[tex]\sf \: a_4 \\ \\ [/tex]
[tex]\sf \: = \: a_3 + d \\ \\ [/tex]
[tex]\sf \: = \: - 5 - 5 \\ \\ [/tex]
[tex]\sf \: = \: - 10 \\ \\ [/tex]
[tex]\sf\implies a_4 = - 10 \\ \\ [/tex]
So, first four terms of an AP series whose first term, a = 5 and common difference, d = - 5 is
[tex]\boxed{ \sf{ \:5, \: 0, \: - 5, \: - 10 \: \: }} \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
↝ nᵗʰ term of an arithmetic progression is,
[tex]\begin{gathered}\bigstar\:\:{\underline{{\boxed{\bf{{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}[/tex]
↝ Sum of n terms of an arithmetic progression is,
[tex]\begin{gathered}\bigstar\:\:{\underline{{\boxed{\bf{{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}[/tex]
Wʜᴇʀᴇ,
Sₙ is the sum of n terms of AP.
a is the first term of the progression.
n is the no. of terms.
d is the common difference.
aₙ is the nᵗʰ term.