Answer
3775
Work Step by Step
The given series = 7, 19, 31, 43
Common difference d = 43 - 31 = 31 - 19 = 19 - 7 = 12
$1^{st}$ term ($a_{1}$) = 7
To solve this type question, first find the $25^{th}$ term, after that find the sum.
$25^{th}$ term = $a_{1}$ + (25 - 1) d
= 7 + 24 $\times$12
= 47+ 288
= 295
Sum of all terms = $\frac{n}{2}$($a_{1}$ + $a_{n}$)
Sum of first 25 terms of given sequence = $\frac{25}{2}$(7 + 295)
= $\frac{25}{2}$(302)
= 25$\times$151
= 3775
