Question

the nth term of an ap is 8-5n find the sum of first seven terms of the ap​

Answer 1

The sum of 7th terms of the AP​ is - 84.

Step-by-step explanation:

Given,

The nth term of an AP = 8 - 5n

To find, the sum of first seven terms of the AP​ $S_{7}=?$

Put n = 1, 2 , 3, 4, ......

The 1st term of an AP = 8 - 5(1) = 8 - 5 = 3

The 2nd term of an AP = 8 - 5(2) = 8 - 10 = - 2

Here, first term(a) = 3, common difference(d) = - 2 - 3 = - 5 and

number of terms(n) = 8

We know that,

The sum of nth terms of the AP​

$S_{n}=\dfrac{n}{2}[2a+(n-1)d]$

The sum of 7th terms of the AP​

$S_{7}=\dfrac{7}{2}[2(3)+(7-1)(-5)]$

$=\dfrac{7}{2}[6+6(-5)]$

$=\dfrac{7}{2}[6-30]$

$=\dfrac{7}{2}[-24]$

= - 84

Hence, the sum of 7th terms of the AP​ is - 84.

Answer 2

$S_7=-84$

Step-by-step explanation:

Given, the nth term of an A.P is 8 - 5n

a₁= 8-5.1 = 8-5 = 3   [ putting n=1]

a₇= 8 - 5.7 = -27

Sum of first 7 terms

$S_n=\frac{n}{2}(a+l)$             a = first term and l = last term and n = number of term

 ∴  $S_7$  $=\frac{7}{2}[3+ (-27)]$

          = - 84