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,..

Question

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Respuesta :

erinna erinna · Answer 1 · 2019-09-17T12:24:50+02:00

Answer:

The 105th term of given sequence is [tex]\frac{105}{2}[/tex].

Step-by-step explanation:

The given sequence is

[tex]\frac{1}{2},1,\frac{3}{2},2[/tex]

It can be rewritten as

[tex]0.5,1,1.5,2[/tex]

Here the first term is 0.5.

It is an arithmetic sequence because it has common difference.

[tex]d=a_2-a_1=1-0.5=0.5[/tex]

[tex]d=a_3-a_2=1.5-1=0.5[/tex]

[tex]d=a_4-a_3=2-1.5=0.5[/tex]

The nth term of an AP is

[tex]a_n=a_1+(n-1)d[/tex]

where, [tex]a_1[/tex] is first term and d is common difference.

Substitute [tex]a_1=0.5[/tex] and [tex]d=0.5[/tex] in the above formula.

[tex]a_n=0.5+(n-1)0.5[/tex]

[tex]a_n=0.5+0.5n-0.5[/tex]

[tex]a_n=0.5n[/tex]

We need to find the 105th term of given sequence.

Substitute n=105 in the above equation.

[tex]a_n=0.5(105)[/tex]

[tex]a_n=52.5[/tex]

[tex]a_n=\frac{105}{2}[/tex]

Therefore the 105th term of given sequence is [tex]\frac{105}{2}[/tex].