Archive for March, 2015

Problem 642

What are the next four terms in the following geometric sequence?
5, 15, 45,…

 

Solution:-

 

First we are find common ratio \frac{15}{5} = 3

In geometric sequence we have to find the next number by multiply last number to common ratio.

45*3 = 135

135 * 3 = 405

405*3 = 1215

1215*3 = 3645

So the next four terms are 135, 405, 1215, 3645

 

Problem 641

What is the common ratio of the following geometric sequence?

5, 15, 45,…

 

Solution:-

 

Common ratio = \frac{second -term}{first-term}

common ratio = \frac{15}{5}

common ratio = 3

Problem 640

Find S10 for -1 + -7 + -13 + -19 +…

 

Solution:-

 

We know S =

    \[ \frac{n}{2}[2a_{1}+(n-1)d]\]

, Where a1 = first term , n = finding term , d = second term – first term.

S10 =  \frac{10}{2}[2*(-1)+(10-1)(-6)]

S10 = -280

So the value of S10  is  -280

problem 639

Find S10 for 2 + 5 + 8 +…

 

Solution:-

 

We know S =  \frac{n}{2}[2a_{1}+(n-1)d] , Where a1 = first term , n = finding term , d = second term – first term.

S10 =  \frac{10}{2}[2*2_{1}+(10-1)3]

S10 = 155

So the value of S10 155.

 

 

Problem 638

Find S25 for \frac{1}{2}+1+\frac{3}{2}+2+...

 

Solution:-

 

We know S =  \frac{n}{2}[2a_{1}+(n-1)d] , Where a1 = first term , n = finding term , d = second term – first term

S25 =  \frac{25}{2}[2*(\frac{1}{2})+(25-1)(\frac{1}{2})]

S25 = \frac{325}{2}

So the value of S25   \frac{325}{2}

 

 

 

 

Problem 637

What is the 20th term of the following arithmetic sequence?

\frac{1}{2},1,\frac{3}{2},2,....

 

Solution:-

 

We know an = a1 + (n -1)*d , Where an = finding term , a1 = first term, d = second term – first term
20th = \frac{1}{2}+(20-1)*\frac{1}{2}
20th = 10
So the value of the 20th term 10.

 

Problem 636

Find the four arithmetic means between 100 and 135.

 

Solution:-

 

In the question first term 100
sixth term 135
a + 5d = 135
100 + 5d = 135
5d = 135 – 100 = 35
d = 7

So the arithmetic mean.
107, 114, 121, 128

 

Problem 635

Find the four arithmetic means between -21 and -36.

 

Solution:-

 

In the question first term -21
sixth term -36
a + 5d = -36
-21 + 5d = -36
5d = -36 + 21 = -15
d = -3

So the arithmetic means are
-24, -27, -30, -33

 

Problem 634

What is the 25th term in the following arithmetic sequence?
-7, -2, 3, 8, …

 

Solution:-

 

We know an = a1 + (n -1)*d ,

Where an = finding term , a1 = first term, d = second term – first term
25th = -7 + (25 – 1) * 5
25th = 113
So the value of 25th term 113

 

Problem 633

What are the next four terms in the following arithmetic sequence?
-7, -2, 3, 8, …

 

Solution:-

 

First we find the value of d = -2 – (-7) = 5
Now we add value of d find the next number
13, 18, 23, 28