Question

Find an explicit formula for the arithmetic sequence 170,85,0,-85,......
d(n)=

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{A.P is 170, 85,0,-85,.......}$

$\underline{\textsf{To find:}}$

$\textsf{Explicit formula for the given A.P}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\textsf{170, 85,0,-85,.......}$

$\textsf{Here, a=170, d=-85}$

$\textsf{n th term of the A.P:}$

$\mathsf{d(n)=a+(n-1)d}$

$\mathsf{d(n)=170+(n-1)(-85)}$

$\mathsf{d(n)=170-85\,n+85}$

$\implies\boxed{\mathsf{d(n)=255-85\,n}}$

$\textsf{which is the required explicit formula}$

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