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Let be in an arithmetic progression of positive terms
MATHEMATICS · Subjective · ISC · Mathematics · Algebra · Algebra
Problem
Let
a
1
,
a
2
,
a
3
,
…
a_1, a_2, a_3, \dots
a
1
,
a
2
,
a
3
,
…
be in an arithmetic progression of positive terms. Let
A
k
=
a
1
2
−
a
2
2
+
a
3
2
−
a
4
2
+
⋯
+
a
2
k
−
1
2
−
a
2
k
2
A_k = a_1^2 - a_2^2 + a_3^2 - a_4^2 + \dots + a_{2k-1}^2 - a_{2k}^2
A
k
=
a
1
2
−
a
2
2
+
a
3
2
−
a
4
2
+
⋯
+
a
2
k
−
1
2
−
a
2
k
2
. If
A
3
=
−
153
A_3 = -153
A
3
=
−
153
,
A
5
=
−
435
A_5 = -435
A
5
=
−
435
and
a
1
2
+
a
2
2
+
a
3
2
=
66
a_1^2 + a_2^2 + a_3^2 = 66
a
1
2
+
a
2
2
+
a
3
2
=
66
, then
a
17
−
a
7
a_{17} - a_7
a
17
−
a
7
is equal to
Related theory
Arithmetic Progressions
Special Series
Special sums
Algebra
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