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3 years ago

The common ratio of a geometric series is 1/4 and the sum of the first 4 terms is 170

Mathematics

2 answers:

nata0808 [166]3 years ago

8 0

Answer:

128

Step-by-step explanation:

As common ratio is 1/4 ; let the first four terms of the geometric series be :

x , 1 / 4 .x , (1 / 4)2 .x , (1 / 4)3 .x or

x , x / 4 , x / 16 and x / 64

Now there sum is 170 , hence

x + x / 4 + x / 16 + x / 64 = 170 or

(64a + 16a + 4a + a ) / 64 = 170 or

85a / 64 = 170

a = 128

Hence first first term of the series is

128

Hitman42 [59]3 years ago

4 0

Answer:

The first term is 128

Step-by-step explanation:please see attachment for explanation

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icang [17]

The explicit rule for given sequence is:

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Further explanation:

We have to determine first of all if the sequence is arithmetic or geometric.

If the difference of two consecutive terms is same then the sequence is arithmetic sequence
If the ratio of two consecutive terms is same then the sequence is geometric sequence

Given sequence is:

12,22,32,42

$a_1=12\\a_2=22\\a_3=32\\.......\\Let\\d=Common\ difference\\d=a_2-a_1=22-12=10\\d=a_3-a_2=32-22=10$

The common difference is 10 which is same for all consecutive terms. So the sequence is an arithmetic sequence.

The general formula for arithmetic sequence is:

$a_n=a_1+(n-1)d\\Here,\\a_n\ is\ the\ nth\ term\\a_1\ is\ the\ first\ term\\d\ is\ the\ common\ difference$

Putting the values of a1 and d

$a_n= 12+(n-1)(10)\\a_n=12+10n-10\\a_n=2+10n$

The explicit rule for given sequence is:

$a_n=2+10n$

Keywords: Arithmetic sequence, Common Difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

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