Question

the 24 term of an AP is twice its 10term show that its 72 nd term is 4 times its 15 term

Answer 1

10th = a+9d ______ (1)
24th = a+23d _____ (2)

Given that,
24th is twice of 10th
that is,
a+23d = 2(a+9d)
a+23d = 2a+18d
-a = -5
a = 5 _____ (3)

Now,
taking out the value of d,
Putting the value of a from (3) to equation (1)&(2)
10th = 5+9d
24th = 5+23d

2(5+9d) = 5+23d
10+18d = 5+23d
5d = 5
d = 1 _____ (4)

by Now,
72th = a+71d
15th = a+14d

we have to prove that,
72th is for times of 15th,

Now,

a+71d = 4(a+14d)
5+71d = 4(5+14d) {a = 5 from (2)}
5+71d = 20+56d
5+(71*1) = 20+(56*1) {d = 1 from (4)}
5+71 = 20+56
76 = 76

Hence proved,

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