Question

What is the last term of the AP? 11, 19,27, 35,

Answer 1

$\sf{\gray{\underbrace{\purple{QUESTION:}}}}$

$\implies$$\bold{What \:is \:the \:last \:term \:of \:the \:AP? \:11, \:19,\:27, \:35,\:}$

$\sf{\gray{\underbrace{\purple{ANSWER:}}}}$

$\bold{Find \:the \:difference \:between \:the \:members\:}$

$\implies$$a2-a1=11-3=8$

$\implies$$a2-a1=11-3=8$

$\implies$$a3-a2=19-11=8$

$\implies$$a4-a3=27-19=8$

$\implies$$a5-a4=35-27=8$

$<b>The difference between every two adjacent members of the series is constant and equal to 8$

$\bold{General \:Form\: an=a1+(n-1)d\:}$

$\implies$$an=3+(n-1)8$

$\implies$$a1=3$

$\implies$$an=35$

$\implies$$d=8$

$\implies$$n=5$

$\bold{Sum \:of \:finite \:series \:members\:}$

$<b>The sum of the members of a finite arithmetic progression is called an arithmetic series.</p><p>Using our example, consider the sum$

$\implies$$3+11+19+27+35$

$<b>This sum can be found quickly by taking the number n of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 3 + 35 = 38), and dividing by 2:$

$\frac{n(a1 + a2)}{2}$

$\frac{5(3 + 35)}{2}$

$<b>The sum of the 5 members of this series is 95</p><p>This series corresponds to the following straight line$ $y=8x+3$

$\bold{Finding \:the \:nth \:element\:}$

$\implies$$a3 =a1+n-1 d =3+3-1 8 =19$

$\implies$$a11 =a1+n-1 d =3+11-1 8 =83$

$\implies$$a19 =a1+n-1 d =3+19-1 8 =147$

$\implies$$a27 =a1+n-1 d =3+27-1 8 =211$