Question

Consider an arithmetic sequence 17/7,20/7,23/7....(a) Write the algebraic expression of this sequence. (b) write the sequence of counting numbers in the abive sequence. Is the newly obtained sequence an ap?

Answer 1

Given:

An arithmetic sequence $\frac{17}{7} ,\hspace{1mm}\frac{20}{7},\hspace{1mm} \frac{23}{7} , ...$

To Find:

(a) Algebraic expression of the sequence,

(b) The sequence of counting number, and the obtained sequence is an AP or not.

Solution:

1st term of the given AP is $\frac{17}{7}$

Common difference in the sequence (r) = $\frac{20}{7} -\frac{17}{7} = \frac{3}{7}$

(a) If $A_{n}$ is the $n^{th}$ term in the sequence then,

$A_{n} = \frac{17}{7} +(n-1) \frac{3}{7}$

$=>\hspace{1mm}7A_{n} = 17+3n-3$

$=>\hspace{1mm}7A_{n} = 14+3n$

∴Algebraic expression of this sequence is, $\hspace{1mm}7A_{n} = 14+3n$.

(b) The sequence of counting numbers is,

$\frac{17}{7} +1, \frac{20}{7} +2, \frac{23}{7} +3,...$

Now, difference between all of them i.e. for two conjugative numbers are same,$\frac{3}{7} +1$.

∴ Yes, the newly obtained sequence is an AP.