Question

if A3 = 22.5 and A13 = 1,328,602.5 Find An There are 3 possible answers!

Answer 1

this is terms of sequance . it may be a arithemetic sequance or geometric sequance.

it is easy to take this sequance as Arithemetic sequance .so i take this as arithemetic sequance.

standard form of An for a arithemetic sequance is An= a+(n-1)d

here a is first term . d is common difference between cocecutive terms.

if mth term is A and nth  term is B , then

d B - A - m

here 3rd term is 22.5 and 13 th term is 1328602.5 . so

$\large d=\frac{1328602.5-22.5}{13-10}=132858$

now

$\large A_n=a+(n-1)132858$

apply A3 = 22.5

$\large 22.5=a+(3-1)132858$

a = 22.5 – 2 * 132858 11 -265693.5

so

$\large A_n=-265693.5+(n-1)132858$

$\LARGE \boldsymbol{A_n=132858n-398551.5}$