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The 14th term of an A.p is 96 while the 25th term is 173 , find a sum of 3rd and 6th term

a + 13d = 96

a + 24d = 173
subtract them:
11d = 77
d = 7
then in a + 13d = 96
a + 91 = 96
a = 5

term(3) = a + 2d = ...
term(6) = a + 5d = ...
now add them

Did you know?

Did you know that in an arithmetic progression (A.p.), each term is obtained by adding a constant difference to the previous term? In this case, the 14th term of the A.p. is 96, and the 25th term is 173. To find the sum of the 3rd and 6th terms, we can use the formula for the nth term of an A.p., which is given by: An = A1 + (n-1)d Using the given information, we can determine the common difference (d) by subtracting the 14th term from the 25th term: 173 - 96 = 77 Now, we can substitute both n = 3 and n = 6 into the formula to find the respective terms: A3 = A1 + (3-1)d = A1 + 2d A6 = A1 + (6-1)d = A1 + 5d Finally, to find the sum of the 3rd and 6th terms, we can add them together: Sum = A3 + A6 = (A1 + 2d) + (A1 + 5d) = 2A1 + 7d So, by substituting the known values for the 14th term (96) and common difference (77) into the formula for the sum, we can determine the sum of the 3rd and 6th terms in this A.p.