Question

-
Find the 6th term of series 1/6, 1/3, 1/2,........ in AP ​

Answer 1

Step-by-step explanation:

PLEASE mark it as brainliest ANSWER

Answer 2

The sixth term of the given sequence is 1

Step-by-step explanation:

Given sequence is $\frac{1}{6},\frac{1}{3},\frac{1}{2},...$ are in AP

To find the sixth term of the given sequence :

• Let $a_1=\frac{1}{6}$ , $a_2=\frac{1}{3}$ ,$a_3=\frac{1}{2}$,...
• Since the given sequence is in AP
• Therefore the common difference $d=a_2-a_1$

• Substitute the values in the formula we get
• $d=\frac{1}{3}-\frac{1}{6}$
• $=\frac{2-1}{6}$
• $=\frac{1}{6}$

The common difference $d=a_3-a_2$

• Substitute the values in the formula we get
• $d=\frac{1}{2}-\frac{1}{3}$
• $=\frac{3-2}{6}$
• $=\frac{1}{6}$

Therefore the common difference is $d=\frac{1}{6}$

The general form of AP is $a_n=a_1+(n-1)d$

• Substitute n=6,$a_1=\frac{1}{6}$ and $d=\frac{1}{6}$ in the above formula
• $a_6=\frac{1}{6}+(6-1)(\frac{1}{6})$
• $=\frac{1}{6}+(5)(\frac{1}{6})$
• $=\frac{1}{6}+\frac{5}{6}$
• $=\frac{1+5}{6}$
• $=\frac{6}{6}$
• $=1$

Therefore $a_6=1$

Therefore the sixth term of the given sequence is 1