Question

Find the seventh term of the series:-
5,14,40,110,.....
Please answer quick
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Answer 1

Answer:

seventh term is 2409..(nearly)

Step-by-step explanation:

$5 \: \: \: 14 \: \: \: \: 40 \: \: \: \: 110 \: \: \: \: \: \\ this \: series \: is \: geometric \: progression \: \\ a = 5 \: \: \: r = \frac{t2}{t1} = \frac{14}{5} = 2.8 \\ tn = a \times {r}^{n - 1} \\ t7 = 5 \times ({2.8)}^{7 - 1} \\ \: \: \: \: = 5 \times {(2.8)}^{6 } \\ \: \: \: \: = 5 \times 481.890304 \\ t7 = 2409.45152 \\ t7 = 2409 \: \: \: \: \: (nearly) \\ seventh \: term \: of \: this \: series \: is \: 2409$

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Answer 2

Answer : -

solution:-

GIVEN : -

let 5,14,40,110 are 1st to 4th term respectively.

first find the ratio between

any two term

Hence R = T2/T1 = 14/5 = 1.8

formula for seventh term is

A to base n = First term ( R ) ^ n-1

A to base 7 = 5 ( 2.8 )^7-1

A to base 7 = 5 ( 2.8 )^6

A to base 7 = 5 ( 481.890304 )

A to base 7 = 2409.45152

hence 7 th term is 2409 or 2410

i hope it helps you.