ARITHMETIC SEQUENCES The first and ninth terms of an arithmetic sequence are $\frac{2}{3}$ $2/3$ and $\frac{4}{5}$ $4/5$ , respectively. What is the fifth term?

Question

Please help ASAP(as soon as possible).
Arithmetic Sequence Formula:
$a$ $a$ sub $n = a$ $n=a$ sub $1 + (n - 1) d$ $1 + (n-1)d$

Breakdown:

a sub n - term you are looking for
a sub 1 - first term in sequence (sorry idk how to format these two properly)
n - the term you are looking for (ex: are you trying to find the second term, third, sixtieth, etc.)
d - common difference.

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Answer 1 · 2018-07-02T13:15:56

$\frac{11}{15}$ $11/15$

Let $d$ $d$ be the common difference of given AP with first term $a = \frac{2}{3}$ $a=2/3$ then ninth term $(n = 9)$ $(n=9)$ of series

$9th term = a + (9 - 1) d$ $\text{9th term}=a+(9-1)d$

$\frac{4}{5} = \frac{2}{3} + 8 d$ $4/5=2/3+8d$

$d = \frac{1}{60}$ $d=1/60$

then the fifth term of given AP

$= a + (5 - 1) d$ $=a+(5-1)d$

$= \frac{2}{3} + 4 (\frac{1}{60})$ $=2/3+4(1/60)$

$= \frac{11}{15}$ $=11/15$