Question

The first four terms of a sequence are 38,32,26 and 20.
(a) find its general term term tn
(B) HENCE FIND THE GENERAL TERM TN, of a sequence if its four terms are
(i) 41,35,29AND 23

Answer 1

Step-by-step explanation:

Given:-

The first four terms of a sequence are 38,32,26 and 20.

To find:-

a) find its general term term tn

(B) HENCE FIND THE GENERAL TERM TN, of a sequence if its four terms are

(i) 41,35,29AND 23

To find:-

The given sequence is 38,32,26,20...

First term (t 1)=38

Second term (t 2) = 32

Common difference (d)=t 2 - t 1

=>d = 38-32=6

=>d = 32-26= 6

=>d=26-20=6

Since the common difference is same through out the series

So They are in the A P.

we know that

the general term of an AP = tn = t 1+(n-1)d

=>tn = 38+(n-1)(6)

=>tn = 38+6n-6

=>tn = 32+6n

General term = tn=6n+32

Answer:-

The general term of the given sequence (AP) is

6n+32

___________________________________

Given:-

The first four terms of a sequence are 41,35,29 and 23

To find:-

find its general term term tn

Solution:-

The given sequence is 41,35,29 and 23

First term (t 1)= 41

Second term (t 2)=35

Common difference (d)=35-41=-6

=>d=29-35=-6

=>d=23-29=-6

Common difference (d)= -6

Since the common difference is same throughout the series.

So they are in the AP

we know that

The general term of the AP = tn = t 1 +(n-1)d

=>tn = 41+(n-1)(-6)

=>tn= 41-6n+6

=>tn=47-6n

Therefore, tn = 47 - 6n

Answer:-

The general term of the given sequence (AP) is

47-6n

Used formula:-

• If" t1 "is the first term and" d "is the common difference and "n" is the number of terms of an AP then the general term of the AP is denoted by tn and defined by t 1+(n-1)d