Question

The sum of the first 5 terms of an arithmetic series is 170. The sum of the first 6 terms is 225. The common difference is 7.

Determine the first 4 terms of the series.

Answer 1

@ganeshie8 @jim_thompson5910 @satellite73

Answer 2

\[S_5 = 2a_1 + (5 - 1)d\]
\[S-6 = 2a_1 + (6 - 1)d\]
u got d .....and S_5 &S_6 so u can easily get a_1 i.e the first term
and after tht get the first four terms

Answer 3

I have learned the summation formula to be \(S_n=\frac{n}{2}(a_1+a_2}. Is this different from what @rishavraj posted?

Answer 4

S5 = sum of the first five terms
S6 = sum of the first six terms

In this case, we're told

S5 = 170
S6 = 225

Subtracting the sums gives

S6 - S5 = 225 - 170 = 55

which is the 6th term. This is because

S6 = (sum of first five terms) + (sixth term)

Answer 5

@calculusxy oops no I forgot to mention n/2

Answer 6

\(S_n = \frac{n}{2}(a_1 + a_n)\)

Answer 7

So then we would have
a_1 + 7(5) = 55
a_1 = 20

Answer 8

And then 20, 27, 34, 41,...

Answer 9

yup

Answer 10

Thanks. And I have noticed that in some problems of arithmetic series, there is a 2a_1 and d(n-1). This is different from what I have learned and I would like to know the difference between them if there is any.

Answer 11

see u know
\[S_n = \frac{ n }{ 2 }(a_1 + a_n)\]
\[a_n = a_1 + (n-1)d\]
so we plug tht value we get
\[S_n = \frac{ n }{ 2 }(a_1 + a_1 + (n - 1)d)\]

Answer 12

So basically the second part of the terms in the parenthesis where there's a_1 repeated and so on, it just is the formula for finding the a_n? Thus, it is the same thing?

And when would I use this formula that has the d with it as opposed to the other one?

Answer 13

see if u got we say S_5 and S_8
bt not the common difference 'd' or the first term 'a'
we only kgot the value of S_5 and S_8
we use tht formula to find a_1 and d ..because in tht case we would be having 2 variables i.e a_1 and d and 2 equations :)

Answer 14

Ok got it! Thanks :)

Answer 15

yw :)))