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The deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is $150, and the deposit for month 5 is $180. Answer the questions below and show all work.

The deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is 150, and the deposit for month 5 is 180. Answer the ques class=

Verified Answer :

Zinethar
  1. 15 dollars
    2. Deposit=15month+105
    3. Deposit=15    12+105=$285
    4.
    500=15month+105
    395=15    month
    26.33=month
    Round up to 27 for the nearest whole month, so month 27.

    Hope this helps!

Answer:

d=$15,

Explicit formula:  @@MATH_TOKEN_0@@

@@MATH_TOKEN_1@@

At 27 month Ginni make a deposit at least $500.

Step-by-step explanation:

Given that the deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is $150, and the deposit for month 5 is $180.

we have to find the common difference i.e d

-- , -- , $150, x, $180 , -------

Let $x be the 4th deposit.

∴ x-150=180-x ⇒ 2x=330 ⇒ x=165

Common difference,d=165-150=$15

Let us find the first tem i.e the value of a

\(a_3=a+(3-1)15\)

⇒ \(150=a+30\thinspace gives\thinspace a=120\)

Explicit formula for arithmetic sequence is

\(a_n=a+(n-1)d\)

⇒ \(a_n=120+(n-1)15\)

Now, we have to find the amount of Ginni in 12th deposit i.e n=12

\(a_{12}=120+(12-1)15\)

⇒  \(a_{12}=120+165=285\)

Now, we have to find at what month Ginni make a deposit at least $500.

@@MATH_TOKEN_8@@

⇒ @@MATH_TOKEN_9@@

⇒ @@MATH_TOKEN_10@@

⇒ @@MATH_TOKEN_11@@

hence, at 27 month Ginni make a deposit at least $500.

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