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3 years ago

The given series has six terms. what is the sum of the terms of the series? 10 + 25 + 40 + . . . + 85

Mathematics

2 answers:

tatiyna3 years ago

4 0

10+25+40+55+70+85
35+95+155
130+155
285

answer: 285

cupoosta [38]3 years ago

4 0

Answer with Step-by-step explanation:

The sum of first n terms of an arithmetic progression is given by:

$S(n)=\dfrac{n}{2}\times (A1+An)$

10+25+40+...+85

Since, the terms have a common difference of 15

So, it is an arithmetic progression of n=6 terms with first term A1=10

and A6=85

We have to find S(6)

$S(6)=\dfrac{6}{2}\times (10+85)$

= 285

Hence, the sum of the terms of the series 10 + 25 + 40 + . . . + 85 is:

285

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Answer:

Step-by-step explanation:

2 (3×-1)=4×-6

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3 years ago

Find the area of the triangle whose base is 12 cm and height is 4 cm.

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Answer:

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3 years ago

Share 1kg in the ratio 4:6.

Lana71 [14]

Answer:

The numerator '4's share is 400 and the denominator '6's share is 600.

Step-by-step explanation:

Step-1: Convert 1kg into grams.

=> 1 kg = 1000 grams

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6 + 4
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Step-3: Divide it with 1000 grams

1000 ÷ 10
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Step-4: Multiply it with each ratio.

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2 years ago

Larry is considering taking out a loan. He estimates that he can afford monthly payments of $265 for 10 years in order to suppor

spayn [35]

Answer:

option-C

option-D

Step-by-step explanation:

we are given

He estimates that he can afford monthly payments of $265 for 10 years in order to support his loan

so, firstly we will find total amount

$A=265\times 12\times 10$

$A=31800$

now, we can verify each options

option-A:

r=6.6% =0.066

Amount is same

$A=31800$

now, we can use APR formula

$A=P(1+\frac{r}{n})^{nt}$

It is compounded monthly

so, n=12

we can plug it and then we can solve for P

$31800=P(1+\frac{0.066}{12})^{12\times 10}$

$P=16465.6215$

we can see that it is less than 24418.05

So, this is FALSE

option-B:

r=6.2% =0.062

Amount is same

$A=31800$

now, we can use APR formula

$A=P(1+\frac{r}{n})^{nt}$

It is compounded monthly

so, n=12

we can plug it and then we can solve for P

$31800=P(1+\frac{0.062}{12})^{12\times 10}$

$P=17133.96$

we can see that it is less than 24418.05

So, this is FALSE

option-C:

r=5.2% =0.052

Amount is same

$A=31800$

now, we can use APR formula

$A=P(1+\frac{r}{n})^{nt}$

It is compounded monthly

so, n=12

we can plug it and then we can solve for P

$31800=P(1+\frac{0.052}{12})^{12\times 10}$

$P=18927.00451$

we can see that it is less than 24418.05

So, this is TRUE

option-D:

r=5.8% =0.058

Amount is same

$A=31800$

now, we can use APR formula

$A=P(1+\frac{r}{n})^{nt}$

It is compounded monthly

so, n=12

we can plug it and then we can solve for P

$31800=P(1+\frac{0.058}{12})^{12\times 10}$

$P=17829.66$

we can see that it is less than 24418.05

So, this is TRUE

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