find n with first term -3, sum is 31.5 and common difference is 2.5

Question

sum of arithmetic sequence is 31.5

Answer 1

Given arithemetic series first term is -3 = a

Common difference is d = t2-t1 = 2.5

Sum = n/2(2a+(n-1)d) = 31.5

n/2(2a+(n-1)d) = 31.5

n(2*-3+(n-1)2.5) = 63

n(-6+2.5n-2.5) = 63

n(2.5n-8.5) = 63

2.5n^2-8.5n-63 = 0

multiple to each side by 10.

25n^2-85n-630 = 0

We can find it another method.

Common difference is 2.5.

Then the given series is would be -3,-0.5,2,4.5,7,9.5,12,14.5,17...

now add the 7 terms -3+(-0.5)+2+4.5+7+9.5+12 = 31.5

So n = 7

 

 

Comments

Your answer is correct.

But you can solve also in first method.

In this case first term is -3, so consider n = 7.

Solution n = 7.