Question

The algebraic form of an arithmetic sequence is 5n+4.
(a) what is its first term?
(b) what is the difference of its 10th and 20th terms?
(c) can the difference of any two terms of this sequence be 368? Justify.

Answer 1

$\sf{\large{\underline {SEQUENCE\: AND \:SERIES}}}$ :

Sequence = 5n + 4

( i ). For first term,

n = 1,

5n + 4 = 5 ( 1 ) + 4

$a_{1}$ = 9

➡️ $\sf{\underline {First \: term}}$,

$\fbox{a_{1} \:=\: 9}$

( ii ). Firstly, we have to find its 10th and 20th term.

For this, we have $a_{1}$ = 9

$\underline{\tt{For \:n\: = \:10}}$ ,

5n + 4 = 5( 10 ) + 4 = 54

$a_{10}$ = 54

$\fbox{a_{10} \:=\: 54}$

Now, $\underline {\tt{For \:n\: =\: 20}}$

$a_{20}$ = 5 ( 20 ) + 4 = 104

$\fbox{a_{20} \:=\: 104}$

️ $\underline {\tt{Difference\:of\:10th\:and\:20th\:terms.}}$

$a_{20}$ - $a_{10}$ = 104 - 54

➡️ $\fbox{\tt{(\:a_{20} \: - \:a_{10} \:) \:= \:50}}$

( iii ). ( iii ). $a_{1}$ = 9

Similarly,

$a_{2}$ = 5( 2 ) + 4 = 14

$a_{3}$ = 5 ( 3) + 4 = 19

Now, $a_{2}$ - $a_{1}$ = 14 - 9 = 5

This forms an A. P. whose Common difference is 5.

Hence, 368 isn't possible to be the difference two terms.

Answer 2

Step-by-step explanation:

. For first term,

n = 1,

5n + 4 = 5 ( 1 ) + 4

a_{1}a

1

= 9