Question

let the greatest common divisor of m,n be 1 if 1/1.7+1/7.13+1/13.19+....up to 20 terms =m/n then 5m+2n =
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Answer 1

The value of 5m + 2n is 342.

Let the greatest common divisor of m,n be 1 if 1/1.7 + 1/7.13 + 1/13.19 + ....up to 20 terms =m/n

We have to find the value of 5m + 2n.

1/1.7 + 1/7.13 + 1/13.19 + .... + 1/[1 + (20 - 1)6][7 + (20 - 1)6]

= 1/1.7 + 1/7.13 + 1/13.19 + .... + 1/115.121

[ Using Ap formula, Tₙ = a + (n - 1)d , to find 20th term of each sequence ]

= 1/6[ (1/1 - 1/7) + (1/7 - 1/13) + (1/13 - 1/19) + ... + (1/115 - 1/121)]

= 1/6[ 1 - 1/121 ]

= 1/6 × 120/121

= 20/121

Here you see, the greatest common divisor of 720 and 121 is 1.

∴ m = 20 and n = 121

now the value of 5m + 2n = 5 × 20 + 2 × 121 = 342

Therefore the value of 5m + 2n is 342.