Thank you for the opportunity to help you with your question. I will try my best to answer your queries below -

1) 5+8+11+ .... +269 = ?

Let's first figure out the number of terms in the sequence

An = A1 + (n-1)*d

269 = 5 + (n-1)*3

n = 89

Sum of the sequence can be given as -> S = n (A1 + An)/2

S = 89* (5+269)/2 = 12193 Answer

2) The given sequence can be written as -

9 + 5 +1 + .............. + (-451) = ? (We got this series by simply replacing the value of K from 1 to 116 in the given summation expression)

-451 = 9 + (n-1)*(-4)

n = 116

S = 116* (9+(-451))/2 = -25636 Answer

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