Question

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) −7, 14 3 , − 28 9 , 56 27 , − 112 81 , ... an = Changed: Your submitted answer was incorrect. Your current answer has not been submitted.

Answer 1

Answer:

an = -7  ×  $(-2/3)^{n-1}$

Step-by-step explanation:

Given data

numbr = n

series = -7, 14/3 , -28/9, 56/27, -112/81 ......................

to find out

a formula for the general term an

solution

we know first term is = -7

second term = 14/3

third term = -28/9

fourth term = 56/27

and so on

so the ratio between these consecutive term i.e second term /first term and third term /second term and fourth term / third term  and so on

ratio are = (14/3)/ -7 and (-28/9)/(14/3) and (56/27) / (-28/9) and so on

ratio are = (-2/3) and (-2/3 ) and (-2/3 ) / (-2/3 ) and so on

here we can see that all ration are same so that an of sequence with ratio -2/3 therefor general formula is for this sequence is given below i.e

an = first term  × n$r^{n-1}$

here r is ratio i.e. -2/3 and n is series 1, 2, 3, 4, 5, 6 ............ an so on

so

an = -7  ×  $(-2/3)^{n-1}$