If P=8+10+12+14+...+108 and Q=4+6+8+10...+106 are sums of arithmetic sequences, determine

pettingyg0

pettingyg0

Answered question

2022-04-24

If P=8+10+12+14++108 and Q=4+6+8+10+106 are sums of arithmetic sequences, determine which of them is greater.

Answer & Explanation

tswe0uk

tswe0uk

Beginner2022-04-25Added 19 answers

For P=8+10+12+14++108
a=8, d=108=2
Let n be total number of terms
108=a+(n1)d
108=8+(n1)2
(n1)2=100
n1=50
n=51
Thus, the sum is:
SP=512(8+108)=2958
For Q=4+6+8+10+106
a=4, d=64=2
Let n be total number of terms
106=a+(n1)d
106=4+(n1)2
(n1)2=102
n1=51
n=52
SQ=522(4+106)=2860
The difference of sums: 29582860=98

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