1. If a,b,c be the 1st, 3rd and nth terms respectively of an A.P., prove that the c2 - a2 sum to n terms is 2 ct a + b- a
Answers
Answered by
1
Answer:
Step-by-step explanation:
Solution
a
1
=a & a
3
=b =a+2d
d=
2
b−a
c=a+(n−1)d
c=a+(n−1)(
2
b−a
)
b−a
2(c−a)
=n−1
b−a
2(c−a)+b−a
=n
S
n
=
2
n
[2a+(n−1)d]
S
n
=
2(b−a)
2(c−a)+b−a
[2a+
(b−a)
2(c−a)
×
2
(b−a)
]=
2
n
[2a+(n−1)d]=
2(b−a)
2(c−a)+b−a
(a+c)
S
n
=
2(b−a)
2(c−a)(c+a)
+
2(b−a)
(b−a)(c+a)
=
b−a
c
2
−a
2
+
2
c+ a
Similar questions