Question

In an A.p 6th term is one more than twice the 3rd term . the sum of the fourth and fifth term is 5 times of 2 term twice . find the 10 th term of the A.p
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Answer 1

Step-by-step explanation:

a6=1+2 (a3)

a+5d=1+2 (a+2d)

a+5d=1+2a+4d

5d-4d=2a-a+1

d=a+1

a4+a5=5 (a2)

a+3d+a+4d=5 (a+d)

2a+7d=5a+5d

7d-5d=5a-2a

2d=3a

2 (a+1)=3a

2a+2=3a

3a-2a=2

therefore a=2

we know that d=a+1, substitute value of 'a'

d=2+1

Hence d=3

a=2 d=3 a10=29

The AP is 2,5,8,11,14,17,20,23,26,29

Sixth term is 1 more than twice third term. a3= 8 and a6=17

Sum of fourth and fifth is five times second term. a4=11 a5= 14 11+14=25

a2=5 so 5×5=25