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If
a_(1)=10 and
a_(n)=3a_(n-1)-5 then find the value of
a_(4).
Answer:

If $a_{1}=10$ and $a_{n}=3 a_{n-1}-5$ then find the value of $a_{4}$ . $\newline$ Answer:

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Find trigonometric ratios using multiple identities

Full solution

Q. If

a_{1}=10

and

a_{n}=3 a_{n-1}-5

then find the value of

a_{4}

.

\newline

Answer:

Given terms: We are given the first term of the sequence, $a_{1} = 10$ , and the recursive formula $a_{n} = 3a_{n-1} - 5$ . To find $a_{4}$ , we need to find the values of $a_{2}$ , $a_{3}$ , and then $a_{4}$ using the recursive formula.
Find $a_{2}$ : First, let's find $a_{2}$ using the recursive formula: $\newline$ $a_{2} = 3a_{1} - 5$ $\newline$ $a_{2} = 3(10) - 5$ $\newline$ $a_{2} = 30 - 5$ $\newline$ $a_{2} = 25$
Find $a_{3}$ : Next, we'll find $a_{3}$ using the value of $a_{2}$ :
$a_{3} = 3a_{2} - 5$
$a_{3} = 3(25) - 5$
$a_{3} = 75 - 5$
$a_{3} = 70$
Find $a_{4}$ : Finally, we can find $a_{4}$ using the value of $a_{3}$ :
$a_{4} = 3a_{3} - 5$
$a_{4} = 3(70) - 5$
$a_{4} = 210 - 5$
$a_{4} = 205$

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