Which term of the sequence 72, 70, 68, 66,…. is 40?
Hint: Find if the given sequence is in A.P. or G.P. and equate the general term formula with the given term to find ‘n’.
The given sequence is 72, 70, 68, 66,…. First, we need to find if it is in A.P. (Arithmetic Progression) or G.P. (Geometric Progression) To find out if the given sequence is in A.P, we need to check if the common difference between two consecutive terms in the sequence is the same for all numbers given in the sequence. Common difference is found by taking any term and subtracting the previous term from it. We need to check the common difference for more than 1 set of consecutive numbers in the sequence. It is denoted as‘d’. If the common difference is the same throughout, then the sequence is in A.P. (Arithmetic Progression). In a G.P. The first term is denoted as ‘a’ and the common ratio is denoted as ‘r’. Common ratio is defined as the ratio between two consecutive terms in the G.P. It will be the same for any two consecutive terms in the G.P. So, first let us check if it is an A.P. d=70-72=-2 d=68-70=-2 a=72, d=-2 …(1) Since, the common difference is the same, it is an A.P. The formula to find the general term in an A.P. is given by $Tn = a + (n - 1)d$ …(2) We are asked to find the value of ‘n’ for the term 40. So, $Tn = 40$ …(3) Substitute (1), (2) in (3) to find the value of ‘n’ $ Tn = a + (n - 1)d \\ 40 = 72 + (n - 1)( - 2) \\ - 2n + 2 = - 32 \\ - 2n = - 34 \\ n = 17 \\ $ We get the value of ‘n’ as 17. So, 40 is the 17th term in the given A.P.
Note: Determine what kind of progression it is. The general term of an A.P. and G.P. must be memorized by the students to solve these kinds of problems quickly and the calculation part must be done carefully to avoid mistakes.