Question

Find the sum of the geometric series
2+6+10+...+58

Answer 1

you sure this is geometric, not arithmetic?

Answer 2

Sorry it is arithmetic

Answer 3

notice from 2 to 6 you add 4, from 6 to 10 you also add 4, so this 4 is the number added to each term in the sequence.
you need to know what term 58 represents, use this formula:
\[\Large{a_n=a_1+d(n-1) -> 58=2+4(n-1) -> n=15}\]

Answer 4

so, you know 58 is the 15th term of this sequence. you want to know the sum of the terms, or the series, when you know the 1st term, the last term, and the total number of terms you can use this formula:
\[\Large{S_n=\frac{(a_1+a_n)n}{2}\\
S_n=\frac{(2+58)15}{2}=450}\]