Question

Is 295 a term of the AP 11,17,23?

Answer 1

Hint: Here the given question is from arithmetic series where we need to see that the given number, belongs to the given series or not, so as to solve for the given question here we need to use the properties of AP which is the formula for the n^th term of the series and then solve accordingly.
Formulae Used: n^th term of an AP series is given by:
\[ \Rightarrow {n^{th}}\,term = a + (n - 1)d\]
Complete step by step answer:
Here in the given question we need to use the formulae for the n^th term of the series, and then we will assume that the given number is the n^th term of the series, and if the formed equation satisfies the values, then the given term belongs to the series.
On solving we get:
\[ \Rightarrow series = 11,17,23...\]
Here first we need to find the common difference that is “d”, on solving we get:
\[ \Rightarrow d = 17 - 11 = 6\]
On solving we get:
\[
   \Rightarrow {n^{th}}\,term = a + (n - 1)d \\
   \Rightarrow 295 = 11 + (n - 1)6 \\
   \Rightarrow (n - 1)6 = 295 - 11 = 284 \\
   \Rightarrow n - 1 = \frac{{284}}{6} = 47.33 \\
   \Rightarrow n = 47.33 + 1 = 48.33 \\
 \]
Here we get the decimal value of the n^th term, hence we get that the given term is not from the given series.

Note: Here the given question is to solve for the n^th term of the given series, in order to get the solution we use the property of the arithmetic series, and after using the formulae we will solve for the question. Here we have used the formulae accordingly and get the decimal value for the n^th term, which satisfied that the given value does not belong to the given term.