How do you find the sum of the first 25 terms of the sequence: 7,19,31,43...?

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Answer 1 · 2018-07-20T20:15:59

#3775#

The given series:

#7, 19, 31, 43, \ldots#

Above series is an arithmetic progression with a common difference

#d=19-7=31-19=43-31=\ldots=12#

First term: #a=7#

The sum of first #n # terms of an AP with term #a# & a common difference #d# is given as

#S_n=n/2(2a+(n-1)d)#

Hence, the sum of first #n=25 # terms of an AP with term #a=7# & a common difference #d=12# is given as

#S_{25}=25/2(2\cdot 7+(25-1)12)#

#=3775#