Question

the nth term of an Ap is tn=3-5n,then the sum of first n term is
1.n/2(1-5n)
2.n(1-5n)
3.n/2(1+5n)
4.n/2(1+n)
​

Answer 1

Answer:

Option 1.

Explanation:

The sum of the first 'n' terms in an A. P. is founding using the formula,

$S_{n} = \frac{n(a+a_{n} )}{2}$

The nth term of an Arithmetic Progression (A.P.), with the first term 'a' and the common difference 'd', is found using,

$a+(n-1)d$

Step 1:

We have been given the nth term of the A. P.,

aₙ = 3 - 5n

Finding the first term by using n = 1,

∴ a₁ = 3 - 5×1 = -2

Step 2:

Now by substituting for a₁ and aₙ in the formula for the sum, we get,

$S_{n} = \frac{n(-2 +3 -5n)}{2}$

$S_{n} = \frac{n(1-5n)}{2}$

Conclusion:

Therefore, the sum of first 'n' terms of the given A. P. is n/2(1-5n).