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If #a_1=5# and #a_i = a_(i-1)+2#, what is the sum of the first 700 terms in the sequence?

Answer 1

Sum of first #n# terms is #492800#

In an arithmetic sequence whose first term is #a_1# and common difference, which is a term in the series "minus" preceding term, the sum of first #n# terms is given by

#S_n=n/2(2a_1+(n-1)d)#

Here as #a_i=a_(i-1)+2#, common difference #d=a_i-a_(i-1)=2# and #a_1=5#,

Hence, #S_700=700/2(2xx5+699xx2)#

= #350xx(10+1398)=350xx1408=492800#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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