Answer:
The sum of first 25 terms = 1050.
Step-by-step explanation:
Given the terms are 6,9,12,15,18,.... in A.P
We have to find the sum of first 25 terms.
Sum of 'n' terms in A.P is
[tex]s_{n} =\frac{n}{2} (2a+(n-1)d)[/tex]
Here 'n' is number of terms
a is first term
d is common difference.
6, 9, 12,15, 18,......,
Here a = 6
d = second term - first term = 9 - 6 = 3
[tex]s_{25} =\frac{25}{2}(2(6)+(25-1)3)[/tex]
[tex]=\frac{25}{2}(12+(24)3)[/tex]
[tex]=\frac{25}{2} (12+72)[/tex]
[tex]=\frac{25}{2} (84)[/tex]
= 25 × 42
= 1050.
Therefore, the sum of first 25 terms = 1050.