1. Solve: 25^2 - 22^2*
Answers
Answer:
25+23+19+16+...+x=115
Its an A.P., where
a=25d=22−25=(−3),S
n
=115
in order to find x, we need to find the number of terms i.e. n
S
n
=
2
n
(2a+(n−1)d)
115=
2
n
(2×25+(n−1)(−3))
115=
2
n
(50+n(−3)−(−3))
115=
2
n
(50−3n+3)
115=
2
n
(53−3n)
115×2=n(53−3n)
230=53n−3n
2
230−53n+3n
2
=0
Here we have a quadratic equation i.e.
3n
2
−53n+230=0
to find the value of n, we need to find the roots of the equation by the formula,
n=
2a
−b±
b
2
−4ac
where a=3,b=−53andc=230
n=
2×3
−(−53)±
(−53)
2
−4×3×230
n=
6
53±
2809−2760
n=
6
53±7
n=
6
53+7
or n=
6
53−7
n=
6
60
or n=
6
46
n=10 or n=7.66
Since the number of terms i.e. n cannot be a decimal number
Therefore n=10
for finding the last term,
x=a+(n−1)d
x=25+(10−1)(−3)
x=25+9(−3)
x=25−27
x=−2
So, the last term of the series i.e. x is −2
Step-by-step explanation:
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