AS sequence

In an arithmetic sequence is given the difference d = -3 and a₇₁ = 455.

a) Determine the value of a₆₂
b) Determine the sum of 71 members.


Correct result:

a₆₂ =  482
s₇₁ =  39760

Solution:

$$\begin{gathered} a_{71}=455;d=-3 \\ {a}_{71}=a_1+(71-1)d \\ 455=a_1+(71-1)\cdot (-3) \\ {a}_1=455-(-210)=665 \\ {a}_{62}=a_1+(62-1)d=665+61\cdot (-3)=482 \end{gathered}$$

$s_{71}=71\cdot {\displaystyle \frac{a_1+a_{71}}{2}}=71\cdot {\displaystyle \frac{665+455}{2}}=39760$

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