reto wrote:

In a certain series, each term is m greater than the previous term. If the 17th term is 560 and the 14th term is 500, what is the first term?

A. 220

B. 240

C. 260

D. 290

E. 305

The detailed explanation

CONCEPT: The series where each terms is more/less than previous term by a constant amount (common difference) resulting in an increasing or decreasing series is called an Arithmetic Progression.i.e. If First term = a and the common difference = d

then the terms in the series can be written as

a, (a+d), (a+2d), (a+3d), (a+4d), (a+5d), (a+6d), (a+7d)...

First term, \(T_1 = a\)

Second term, \(T_2 = (a+d)\)

Third term, \(T_3 = (a+2d)\)

Forth term, \(T_4 = (a+3d)\)

...

i.e. nth Term of the series,\(T_n = a+(n-1)d\)Here the question has mentioned that common difference = m

i.e. 17th Term, \(T_{17} = a+(17-1)m = a+16m = 560\) -------- Equation (1)

and 14th Term, \(T_{14} = a+(14-1)m = a+13m = 500\) -------- Equation (2)

Subtract the second equation from the first

i.e. \((a+16m) - (a+13m) = 560 - 500\)

i.e. \(3m = 60\)

i.e. \(m = 20\)

Substituting in Equation (2), we get

\(a + 13*20 = 500\)

i.e. \(a = 500 - 260 = 240\)Answer: option

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