What is the explicit formula in "29, 229, 429, 629..."?

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Answer 1 · 2018-07-25T13:53:41

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The given series:

#29, 229, 429, 629, \ldots#

The difference of consecutive terms

#229-29=429-229=629-429=\ldots=200#

The given series is an arithmetic progression with first term #a=29# & a common difference #d=200#

Now, the #n#th term of given series

#T_n=a+(n-1)d#

#=29+(n-1)200#

#=29+200(n-1)#

Now, the sum of first #n#th terms of given series

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

#=n/2(2\cdot 29+(n-1)200)#

#=n( 29+100 (n-1))#