Question

⅙ ⅓ ½ find the next four terms of A p​

Answer 1

Step-by-step explanation:

$Given A.P is</p><p></p><p> </p><p></p><p>−1,41,23,....</p><p></p><p> </p><p></p><p> the common difference of an  A.P is given by d=an+1−an</p><p></p><p>by putting n=1 in above equation</p><p></p><p>d=a2−a1=(41)−(−1)</p><p></p><p>d=41+1</p><p></p><p>d=45</p><p></p><p> </p><p></p><p>first term of this A.P is</p><p></p><p>a1=−1</p><p></p><p> </p><p></p><p>the nth term of this A.P is given by</p><p></p><p>an=a1+(n−1)d</p><p></p><p>⟹an=−1+(n−1)(45)</p><p></p><p>⟹an=−1+45n−45</p><p></p><p></p><p></p><p>⟹an=−49+45n….eq(1)</p><p></p><p> </p><p></p><p>finding next four terms of A.P</p><p></p><p> </p><p></p><p>1)     for finding the 4th term of sequence (a4)  put n=4 in eq(1)</p><p></p><p>⟹a4=4−9+45×4</p><p></p><p>⟹a4=4−9+420</p><p></p><p>⟹a4=411</p><p></p><p> </p><p></p><p>2)     for finding the 5th term of sequence (a5)  put n=5 in eq(1)</p><p></p><p>⟹a5=4−9+45×5</p><p></p><p>⟹a5=4−9+425</p><p></p><p>⟹a5=416</p><p></p><p>⟹a5=4</p><p></p><p></p><p></p><p>3)    for finding the 6th term  of sequence (a6) put n=6 in eq(1)</p><p></p><p>⟹a6=4−9+45×6</p><p></p><p>⟹a6=4−9+430</p><p></p><p>⟹a6=421</p><p></p><p> </p><p></p><p>4)    for finding the 7th term of sequence (a7) put n=7 in eq(1)</p><p></p><p>⟹a7=4−9+45×7</p><p></p><p>⟹a7=4−9+435</p><p></p><p>⟹a7=426</p><p></p><p>⟹a7=213</p><p></p><p>Answer ByToppr</p><p></p><p>SHARE</p><p></p><p>How satisfied are you with the answer?</p><p></p><p>This will help us to improve better</p><p></p><p>ASK</p><p></p><p>Get Instant Solutions, 24x7</p><p></p><p>No Signup required</p><p></p><p></p><p></p><p></p><p>$

The first 4 terms of the sequence is given. Let us examine what type of sequence is it and find the general term of the sequence by which we can generate any term of the sequence.

Let us find the the Least Common Multiple( or LCM) of denominators of the first 4 terms given:

The denominators of the 4 terms are 6,3,2,3 and obviously 6 is the LCM. Now let us convert the terms into equivalent fractions with denominators as 6,the LCM.

Then the 1st term of sequence is 1/6 = 1/6

2nd term of the sequence =1/3= 2/6

3rd term=1/2=3/6

4th term=2/3=4/6

Obviously the numerator is increasing by one. So the value of each next term increase by 1/6

Therefore the seqence is in arithmetic progression (or AP) with common difference of the sequence is1/6 , and the starting term is 1/6. Therefore, the genaral nth term of the sequence = starting term+(n-1)*common difference= 1/6+(n-1)(1/6)=n/6. So any term of the sequence {n/6} can easily be generated by givin n a suitable value.

The next term is 5th and 6th are got by putting n=5 and n=6

So the 5th term = 5/6

The 6th term = 6/6=1