how we find the 11 term of A.P whose firsts term is 5 and d is -3??
Answers
Answer:
2 is the common difference of an AP .
Given:
a (first term of the arithmetic progression) = 5
S_{4}=\frac{1}{2}(S_{8}-S_{4})S
4
=
2
1
(S
8
−S
4
)
To find:
d (Common Difference) = ?
Solution:
The general sequence of an AP is a ,a + d ,a + 2d ,a + 3d,…
Substituting a=5 then
5, 5 + d,5 + 2d,5 + 3d,5 + 4d,5 + 5d,5 + 6d,5 + 7d,,..
Let the first 4 terms be 5,5 + d,5 + 2d,5 + 3d
And let the next 4 terms be = 5 + 4d,5 + 5d,5 + 6d,5 + 7d
And \bold{S_{4}=\frac{1}{2}(S_{8}-S_{4})}S
4
=
2
1
(S
8
−S
4
) ----(1)
By substituting these values in (1)
\begin{gathered}\begin{array}{l}{5+5+d+5+2 d+5+3 d} \\ {\qquad \qquad=\frac{1}{2}(5+4 d+5+5 d+5+6 d+5+7 d)}\end{array}\end{gathered}
5+5+d+5+2d+5+3d
=
2
1
(5+4d+5+5d+5+6d+5+7d)
20+6d=10+11d
10=5d
d=2
Therefore, the common difference = 2
\begin{gathered}\\\\\\\end{gathered}
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aₙ=a+(n-1)d
a₁₁=a+10d
a₁₁=5-(10)(-3)
a₁₁=5-30
a₁₁=-25