A term is said to be the nth term from the end of an arithmetic progression when counting backward from the last term and finding the required term at that position. For example counting 3 terms from the end means getting the third last term of A.P.
An arithmetic progression is a sequence where the difference between consecutive terms remains constant. The constant difference is called common difference denoted by ‘d’. The first term is denoted by ‘a’. If ‘n’ represents the number of terms then the last term is denoted by ‘l’. The nth term of an A.P is denoted by ‘an’.
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Given A.P.: -11, -8, -5, …, 49
Common difference d = -8 – (-11) = 3
Last term aₙ = 49
Using first term a₁ = -11 and d = 3, find n:
aₙ = a₁ + (n-1)d
49 = -11 + (n-1)3
49 + 11 = 3(n-1)
60 = 3(n-1)
20 = n-1
n = 21
Therefore total terms = 21
4th term from end means:
Position from beginning = n – 3 = 21 – 3 = 18th term
Using arithmetic sequence formula:
a₁₈ = a₁ + (18-1)d
= -11 + (17)3
= -11 + 51
= 40
Hence, 40 is the correct answer.
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