1Find the number of terms of the arithmetic sequence with th

1-Find the number of terms of the arithmetic sequence with the given description that must be added to get a value of 3360.

The first term is 5, and the common difference is 2

2-The purchase value of an office computer is $14,000. Its annual depreciation is $1790. Find the value of the computer after 5 years.

1) S_n = 3360

a₁ = 5, d = 2

Now S_n = (n/2){2a₁ + (n-1)d}

=> 3360 = (n/2)[10+(n-1)2]

=> 3360 = (n/2)[2n+8]

=> 3360 = n² + 4n

=> n² + 4n-3360 = 0

=> n²+60n-56n-3360=0

=> n(n+60)-56(n+60) = 0

=> (n+60)(n-56) = 0

=> n=-60, 56

As n can not be negative, so n = 56

2) Here a₁ = 14,000

d = -1790

And n = 5

So by general formula for n^th term of arithmetic sequence gives:

a_n = a₁ + (n-1)d

=> a₅ = 14000+(5-1)(-1790)

=> a₅ = 14000-7160

=> a₅ = 6840

Hence the value of computer after 5 years = $6840