Answer:
[tex]S_{25}=555[/tex]
Step-by-step explanation:
Given that,
In an AP, the 6th term is 39 i.e.
[tex]a_6=a+5d\\\\39=a+5d\ ....(1)[/tex]
In the same AP, the 19th term is 7.8 i.e.
[tex]a_{19}=a+18d\\\\7.8=a+18d\ ......(2)[/tex]
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 :
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Put n = 25 and respected values,
[tex]S_{25}=\dfrac{25}{2}[2(51)+24(-2.4)]\\\\=555[/tex]
Hence, the sum of first 25 terms of the AP is equal to 555.
