[tex]{\Large{\boxed{\boxed{\mathrm{\pink{Question :}}}}}} \\ [/tex]
In an Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively.
Find the :
(i) first term
(ii) common difference
(iii) sum of the first 20 terms
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Answer:
a = 24
d = - 2
S₂₀ = 100
Step-by-step explanation:
Given ;
\begin{gathered}\displaystyle{t_4=18}\\\\\\\displaystyle{t_6=14}\\\\\\\displaystyle{We \ know \ term \ formula}\\\\\\\displaystyle{t_n=a+(n-1)d}\\\\\\\displaystyle{t_4=a+(4-1)d}\\\\\\\displaystyle{18=a+3d}\\\\\\\displaystyle{a=18-3d \ ..(i)}\\\\\\\displaystyle{t_6=a+(6-1)d}\\\\\\\displaystyle{14=a+5d}\\\\\\\displaystyle{a=14-5d \ ..(ii)}\end{gathered}
t
4
=18
t
6
=14
We know term formula
t
n
=a+(n−1)d
t
4
=a+(4−1)d
18=a+3d
a=18−3d ..(i)
t
6
=a+(6−1)d
14=a+5d
a=14−5d ..(ii)
Step-by-step explanation:
Question :
In an Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively.
Find the :
(i) first term
(ii) common difference
(iii) sum of the first 20 terms
Solution :
Subtracting Equation 1 from Equation 2 we get,
Where,
Sn = Sum of numbers
n = no. of terms
a = first term
d = common difference
Putting the values in the given formula