Question

Consider the arithmetic sequence 97, 94, 91 · · · a) What is the common difference of this sequence ? b) Write the algebraic form of this sequence c) Which is smallest positive term of this sequence ? d) How many positive terms are there in this sequence ?

Answer 1

Answer:

a) d=-3

b) 94+2n-2

d) 32

Step-by-step explanation:

Answer 2

$Given \: Arithmetic \: sequence :$

$97,94,91,\ldots$

$First \: term (a) = a_{1} = 97$

$a.)\red{Common \: difference (d) }$

$= a_{2} - a_{1}$

$= 94 - 97$

$\green { = -3}$

$\red{ n^{th} \:term \: of \: an \:A.P \: (a_{n})}$

$= a + (n-1)d$

$= 97 + (n-1) (-3)$

$= 97 - 3n + 3$

$= 100 - 3n$

$\green { \therefore Algebraic \:form \: of \: this}$

$\green { sequence (a_{n} ) = 100 - 3n }$

$\red{ c. The \: smallest \: positive \:term }$

$Take \: a_{n} = 0$

$\implies 100 - 3n = 0$

$\implies - 3n = -100$

$\implies n = \frac{-100}{-3}$

$\implies n = 33.3\bar{3}$

$\implies n = 33 \: \blue { ( Integral \:part ) }$

Therefore,

$\red{ The \: smallest \: positive \:term}$

$a_{33} = 100 - 3 \times 33$

$= 100 - 99$

$\implies a_{33} \green {= 1 }$

$\red{ d . Number \: of \: positive \: terms \: in }$

$\red{ in \:this \: sequence } \green { = 33 }$

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