Question

The first two terms of an arithmetic series are
-
2
and 3. How many terms are needed for the sum to equal 306 ?

Answer 1

Let's call the common difference in the arithmetic series d. In this case, d = 3 - (-2) = 5. The formula for the sum of an arithmetic series is given by:

Sum = n*(a1 + an) / 2,

where a1 is the first term, an is the nth term, and n is the number of terms.

We know that the first term a1 = -2, and we have to find the number of terms n such that Sum = 306.

We also know that an = a1 + (n-1) * d. Substituting a1 and d in this formula, we get:

an = -2 + (n-1) * 5.

Now we can substitute a1 and an in the formula for the sum:

306 = n*(-2 + (-2 + (n - 1) * 5)) / 2.

Simplifying and solving for n, we get:

306 = n*(n*5 - 4) / 2.

612 = n*(5n - 4).

At this point, you may try out different values of n to see which one satisfies the above equation. If you try n = 6, you'll get 612 = 6 * 26, which is true. Therefore, n = 6 is the answer.

So, 6 terms are needed for the sum to equal 306.