Question

Please help with this

Answer 1

Answer:

$S_{25}=555$

Step-by-step explanation:

Given that,

In an AP, the 6th term is 39 i.e.

$a_6=a+5d\\\\39=a+5d\ ....(1)$

In the same AP, the 19th term is 7.8 i.e.

$a_{19}=a+18d\\\\7.8=a+18d\ ......(2)$

Subtract equation (1) from (2).

7.8 - 39 = a+18d - (a+5d)

-31.2 = a +18d-a-5d

-31.2 = 13d

d = -2.4

Put the value of d in equation (!).

39 = a+5(-2.4)

39 = a- 12

a = 39+12

a = 51

The sum of n terms of an AP is given by :

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

Put n = 25 and respected values,

$S_{25}=\dfrac{25}{2}[2(51)+24(-2.4)]\\\\=555$

Hence, the sum of first 25 terms of the AP is equal to 555.