Question

Time to run your Brains. I need step-by-step explanation.

Answer 1

Given: The series 1, 5, 7, 11, ...............77.

To find: How many terms are there in the series?

Solution:

• Now we have given the series: 1, 5, 7, 11, ...............77.

• We have two series in this:

                  1, 7, .........

                  5, 11, ...............77

• In both series common difference is 6. In both series the number of terms will be same because the last term of first series is in the second series and first term of first series is outside the second series.

• Consider second series, we get: 5, 11, ...............77

                  a(n) = a + (n-1)d

                  77 = 5 + (n-1)6

                  72/6 = n - 1

                  12 = n - 1

                  n = 13

• So in second series, the number of terms are 13.

• Similarly, the first series is having 13 terms.

Answer:

              So the number of terms are 26.