Question

series help

Answer 1

@plohrr There must be 3rd term given, lest it cant be deduced

Answer 2

but that is the whole question

Answer 3

195

390

780

1125

Answer 4

Let's call the first term of the series \(a_1\). Since this is an arithmetic series, there is a common difference between successive terms, which I'll call \(d\).

In other words, the second term is \(a_2=a_1+d\), the third is \(a_3=a_2+d=a_1+2d\), and so on. Generally, \(a_n=a_{n-1}+(n-1)d\).

Now you can find each term in between, then add them up. I think there's a simpler method involving some formula, but I don't remember it...

Answer 5

so i would sub the values in

Answer 6

Sorry, that formula should be \(a_n=a_1+(n-1)d\).

Answer 7

Well first you find the common difference \(d\). From the formula, you have
\[a_{10}=a_1+9d~~\Rightarrow~~75=3+9d\]

Answer 8

a10 be the 10th term and a be 1st term.
so using the formula of AP we get a10=a+(10-1)*d , where d is the common difference
so 75=3+9*d
or,d=72/9=8
Now,using the sum of the series formula, S=n/2(a+a10)
S=(10/2)*(3+75)
s=5*78
S=390

@plohrr Please do read the step mentioned by @SithsAndGiggles

Answer 9

thanks guys!