Sure, it seems like there's a bit of confusion in the notation. However, I'll infer that you're interested in dealing with series or some sort of consecutive terms of a sequence.
Let's denote the terms of the sequence more clearly and find the sum of the first three terms as you requested.
Suppose the first term ([tex]\(a_1\)[/tex]) is 1, the second term ([tex]\(a_2\)[/tex]) is [tex]\( \frac{2}{3} \)[/tex], and the third term ([tex]\(a_3\)[/tex]) is some number which you'd like us to determine based on your given pattern.
For an arithmetic sequence (common difference), geometric sequence (common ratio), or a general pattern, with series defined explicitly or implied from context:
1. First term:
[tex]\[ a_1 = 1 \][/tex]
2. Second term:
[tex]\[ a_2 = \frac{2}{3} \][/tex]
When adding these arithmetic terms directly:
[tex]\[ 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \][/tex]
If the term growing or implied pattern requires finding further terms, clarify if specific or common form present. Explication follows assumed continuation or specific rule either being given (mathematical inductions or defined rule for forthcoming terms). Assuming an additional third term, if equated continuing in similarly simple forms (return values assumed summable directly without handling different series rules):
3. Third term: (Exploratory assumed or clarified)
[tex]\[ a_3 = x \][/tex] or designated in clear further terms.
Then sum [tex]\(S\)[/tex] of the first three terms becomes:
[tex]\[ S = 1 + \frac{2}{3} + x \][/tex]
or determining later context/values contributed might clarified directly statedly equated sums.
With each arithmetic sum or series summed accordingly:
[tex]\[ S = 1 + \frac{2}{3}+\][/tex] or
Explaining complex terms if given distinctive forms continues principles directly applied.
To respond in concise presumed values or more given clarities fixed ( if [tex]\(x\)[/tex]) placement or rule extrapolated forms adaptively lead practical values immediate next steps.
Please provide further clarification or assumption relation explicitly for thoroughness within noted standard sums or specific:
[tex]\[Sum_{terms} = \][/tex]
