Question 690880
Find the sum of the first 196 terms of 2,7,12,17,.. I cant seem to figure this problem out 



This is an arithmetic sequence, or A.P., and the formula for sum of an A.P.: {{{S[n] = (n/2)(2a[1] + (n - 1)d)}}}, with {{{S[n] = S[196]}}}, 1st term, or {{{a1]}}} = 2; n, or amount of terms to be summed = 196, and d, or common difference = 5
 

Therefore, {{{S[n] = (n/2)(2a[1] + (n - 1)d)}}} becomes: {{{S[196] = (196/2)(2(2) + (196 - 1)5)}}}


{{{S[196] = 98(4 + (195)5)}}}


{{{S[196] = 98(4 + 975)}}}


{{{S[196] = 98(979)}}}


{{{S[196]}}}, or sum of the 1st 196 terms in the series = {{{highlight_green(95942)}}}


You can do the check!!


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