Question

if nth term of a sequence is 2n2+1/2n2-1 find t4+t7+t10=S​

Answer 1

Given: nth term of a sequence is 2n²+1 / 2n²-1

To find: t4 + t7 + t10 = S​

Solution:

• As we have given that nth term of a sequence is 2n²+1 / 2n²-1, this means:

              a(n) = a + (n-1)d = 2n²+1 / 2n²-1

• So from this expression, we can find the values of t4, t7 and t10.

• Finding value of t4, put n = 4 we get:

            t(4) = 2(4)² + 1 / 2(4)² - 1

                  = 32 + 1 / 32 - 1

                  = 33/31

• Finding value of t7, put n = 7 we get:

            t(7) = 2(7)² + 1 / 2(7)² - 1

                  = 98 + 1 / 98 - 1

                  = 99/97

• Finding value of t10, put n = 10 we get:

            t(10) = 2(10)² + 1 / 2(10)² - 1

                    = 200 + 1 / 200 - 1

                    = 201/199

• Now adding all the terms we get:

                   = 33/31 + 99/97 + 201/199

                   = 636999 + 610731 + 604407 / 598393

                   = 3.09518

Answer:

         So, the value of t4+t7+t10 is 3.09518.