Question

The 4 th term of an AP is equal to 3 times the first term and 7th term exceeds which the 3 rd term by 1 . Find its n th term

Answer 1

4th term=
an= a+ (n-1)d= a+ (4-1)d=a+3d
first term = a
CASE1 ATQ,
a+3d= 3(a)
a+3d= 3a
3d= 3a-a
3d= 2a
d= 2a/3


a6= a+6d= 7th term.
a3= a+2d
ATQ,CASE2
a7= a3+1
a+6d= a+2d+1
a gets cancelled because if we will take a on the other side then a becomes -a and as we know a-a=0
6d-2d=1
4d=1
4(2a/3)=1
8a/3=1
a= 3/8
putting value of a in d
d= 2(3)/8
----------------
3
3/4×1/3
d=1/4

an= a+ (n-1)d
an= 3/8+ (n-1)1/4
an= 3/8+ 1/4n-1/4
an= 3+ 2n-2/8
an= 1+2n/8


hope it helps.
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