Given the progression 5, 8, 11, 14. . .?

Question

Can u answer this for me. and please show me how u did it and the formula u used. thanks!!

Given the progression 5, 8, 11, 14..

- What is the 25th term??

- What is the sum of the first 25 terms?

(what is this anyway, geometric series, progression??)

and another one..

- How many terms of the sequence -9, -6, -3,... must be added so that the sum is 66?

Please show me how u did it. THANKS A LOT! *winks*

Answer 1

This is a plain old sequence. You should note that each term after the first is 3 more than the last. So the initial term is 5 and the difference is +3. Rather than using fingers and toes to solve the questions you pose, there are formulas. Since the second term is 5 +(2-1) 3, the same formulation will hold for all others. So the 25 term is 5+ 24*3 or 77. To find the sum, you can show the result in general is
n(To) + AD(sum 1.....n-1)= n(To) + AD (n)(n-1)/2
where n is the number of terms, To is the first term, and AD is the arithmetic difference. In this problem, To= 5, AD=3 and n= 25. Substiuting, I get 1025.

In problem 2, you have the sum, To and Ad. You have to find n. Probably a trial and error solution will work best here with the above formula.

Answer 2

The sequence is the previous number + 3
The other is the same.
the 25th term is 5, 8... ([25-1]*3)+ 5
= 77
As for the sum, use the calculator because I do not know yet*.

Well, -9, -6, -3,...66 is (66/3)+3 = 25
because of the 22nd term of three is equivalent to 66

Answer 3

this is an AP,COMMON DIFFERENCE=3

FORMULA:a+(n-1)d a=5,n=25,d=3,This gives u the 25th term.do it yourself.

summation:n/2{2a+(n-1)d}
n=25,a=5,d=3 find out the ans urself.

u have 2 form an eqn where n is the variable.

n/2{2x-9+(n-1)3}=66.......from the 1st formula.

ans 1:77
ans 2:1025
ans 3:n=11

Answer 4

geometric series does not require too much knowledge. only patience and common sense...good luck

Answer 5

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