Question

Find
the number of the term
18, 15 1/2, 13.......-47

​

Answer 1

Answer:

A=18

d =-5/2

an=-47

an=a+(n-1)d

-47=18+(n-1)-5/2

-47-18=n-1(-5/2)

-65*-2/5=n-1

-13*-2

26+1 =n

27=n

Answer 2

$\Large{\underline{\underline{\bf{Given:-}}}}$

$first \: term \: (<strong>a</strong>) = 18 \\ \\common \: difference \: (d) = a_2 - a_1 \\ \\ = 15 \frac{1}{2} - 18 \\ \\ = \frac{31}{2} - 18 \\ \\ = \frac{31 - 36}{2} \\ \\ = \frac{ - 5}{2} \\ \\n ^{th} \: term \: of \: airthmetic \: progression \: series \: ( a_n )= - 47$

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$\Large{\underline{\underline{\bf{To \: Find:-}}}}$

$n \: = \: ?$

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${\bold{\underline{\underline{As \: we \: know \: , \: for \: an \: airthmetic \: progresssion :-}}}}$

$</u></strong><strong><u>⟹</u></strong><strong><u>a_n = a + (n - 1)d \\ \\ </u></strong><strong><u>⟹</u></strong><strong><u>- 47 = 18 + (n - 1) \frac{ - 5}{2} \\ \\</u></strong><strong><u>⟹</u></strong><strong><u> - 47 - 18 = (n - 1) \frac{ - 5}{2} \\ \\</u></strong><strong><u>⟹</u></strong><strong><u> - 65 = (n - 1) \frac{ - 5}{2} \\ \\</u></strong><strong><u>⟹</u></strong><strong><u> \frac{ - 65 \times 2}{ - 5} = (n - 1) \\ \\ </u></strong><strong><u>⟹</u></strong><strong><u>\frac{ - 130}{ - 5} = (n - 1) \\ \\ </u></strong><strong><u>⟹</u></strong><strong><u>26 = n - 1 \\ \\</u></strong><strong><u>⟹</u></strong><strong><u> 26 + 1 = n \\ \\ </u></strong><strong><u>⟹</u></strong><strong><u>27 = n$

$\huge\boxed{n \: = \: 27}$

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${\bold{\underline{\underline{Therefore \: , \: this \: given \: Airthmetic \: progression\: has \: 27 \: terms \: in \: it:-}}}}$

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$\Large{\underline{\underline{\bf{Thanks:-}}}}$