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.


Result

a62 =  482
s71 =  39760

Solution:

a71=455;d=−3 a71=a1+(71−1)d 455=a1+(71−1)⋅(−3) a1=455−(−210)=665  a62=a1+(62−1)d=665+61⋅(−3)=482a_{ 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
s71=71⋅a1+a712=71⋅665+4552=39760s_{ 71 } = 71 \cdot \dfrac{a_1+a_{ 71 }}{2} = 71 \cdot \dfrac{ 665 + 455 }{2} = 39760

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