Question

In an arithmetic​ sequence, the nth term an is given by the formula an=a1+(n−1)d​, where a1 is the first term and d is the common difference.​ Similarly, in a geometric​ sequence, the nth term is given by 1an=a1•rn−1​,

where r is the common ratio. Use these formulas to determine

the indicated term in the given sequence.

The 105th term of 1/2, 1, 3/2, 2,..

Answer 1

Answer:

105th term of given series is

$a_n=\dfrac{105}{2}$

Step-by-step explanation:

Given series is

$\dfrac{1}{2},\ 1,\ \dfrac{3}{2},\ 2,\ \dfrac{5}{2}.....$

As we can see,

$\textrm{First term},a_1=\dfrac{1}{2}$

Also,

$1-\dfrac{1}{2}=\dfrac{3}{2}-1=2-\dfrac{3}{3}=.....=\dfrac{1}{2}$

hence, we can say given series is in arithmetic progression,

with common difference,

$d=\ \dfrac{1}{2}$

As given in question the nth term in A.P is given by

$a_n=a_1+(n-1)d$

since we have to find the 105th term, so we can write

   $a_{105}=\dfrac{1}{2}+(105-1)\dfrac{1}{2}$

              $=\dfrac{1}{2}+\dfrac{104}{2}$

              $=\dfrac{105}{2}$

Hence, the 105th term of given series of A.P is $\dfrac{105}{2}$.