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In an arithmetic sequence whose 4th term is 14 and whose 11th term is 70, the fi...


Question

In an arithmetic sequence whose 4th term is 14 and whose 11th term is 70, the first term and common difference are

Options

A) a = -10, d = 8

B) a = -7, d = 7

C) a = 10, d = 8

D) a =-14, d = 7

The correct answer is A.

Explanation:

\(a_4 = a+3d = 14\) ..... (1)
\(a_{11} = a+10d = 70\) ..... (2)
Solve simultaneously, subtract equation (1) from (2)
\(7d = 56\)
\(d = \cfrac{56}{7} = 8\)
\(a+3(8)=14\)
\(a=14-24=-10\)

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Discussion (2)

  • \(a_4 = a+3d = 14\) ..... (1)
    \(a_{11} = a+10d = 70\) ..... (2)
    Solve simultaneously, subtract equation (1) from (2)
    \(7d = 56\)
    \(d = \cfrac{56}{7} = 8\)
    \(a+3(8)=14\)
    \(a=14-24=-10\)

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  • Ademurewa

    The answer is a

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