if d=3 first term is -2 then find the sum of
first 5terms
Share
if d=3 first term is -2 then find the sum of
first 5terms
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
given ; d=3 , a1 =-2
sum of 5 terms means take n = 5
sn = n/2 {2a+(n-1)d}
s5 = 5/2 {2×-2+(5-1)3}
s5 =5/2 {-4+4×3}
s5 =5/2 {-4+12}
s5 = 5/2 (8)
s5 = 40/2
s5=8
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
First term of an AP, a = - 2
Common difference of an AP, d = 3
Number of terms, n = 5
We know,
↝ Sum of n terms of an arithmetic sequence 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 sequence.
n is the no. of terms.
d is the common difference.
So, on substituting the values, we get
[tex]\sf \: S_5 = \dfrac{5}{2} \bigg(2 \times ( - 2) + (5 - 1) \times 3\bigg) \\ \\ [/tex]
[tex]\sf \: S_5 = \dfrac{5}{2} \bigg( - 4 + 4 \times 3\bigg) \\ \\ [/tex]
[tex]\sf \: S_5 = \dfrac{5}{2} \bigg( - 4 + 12\bigg) \\ \\ [/tex]
[tex]\sf \: S_5 = \dfrac{5}{2} \times 8\\ \\ [/tex]
[tex]\sf \: S_5 = 5 \times 4\\ \\ [/tex]
[tex]\sf \: \bf\implies \:S_5 = 20\\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
↝ nᵗʰ term of an arithmetic sequence is,
[tex]\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}[/tex]
Wʜᴇʀᴇ,
aₙ is the nᵗʰ term.
a is the first term of the sequence.
n is the no. of terms.
d is the common difference.