Question

The sum of the first 20 terms of the series: \(2^2 + 5^2 + 8^2 + \dots\), is:

• A. 25830
• B. 24450
• C. 24570
• D. 24590

Hint:

In series questions, identify if the terms follow an arithmetic or geometric progression, then use the appropriate formula for the sum of the terms.

Answer 1

The Correct Option is D

The given series is \( 2^2 + 5^2 + 8^2 + 11^2 + \dots \). This is a sequence of squares of terms in an arithmetic progression (A.P.) where the first term is 2 and the common difference is 3. To find the sum of the first 20 terms, we use the formula for the sum of squares of the terms in an A.P.:
\[ S$_$n = n \times \left( a^2 + d^2 \times \frac{(n-1)(3n-1)}{6} \right) \] where \(a\) is the first term, \(d\) is the common difference, and \(n\) is the number of terms. Substituting the values for \(a = 2\), \(d = 3\), and \(n = 20\), we compute the sum, which results in 24590.
Thus, the correct answer is 24590.