What comes next in the sequence: 2, 6, 12, 20, 30, ____?

Mathematics
What comes next in the sequence: 2, 6, 12, 20, 30, ____?

ScanSolve AI Answer

Answer

42\text{42}

Step 1: በተከታታይ ቁጥሮች መካከል ያለውን ልዩነት እንፈልግ። The differences between consecutive terms are: 62=46 - 2 = 4 126=612 - 6 = 6 2012=820 - 12 = 8 3020=1030 - 20 = 10

Step 2: የልዩነቶቹን ቅደም ተከተል እንመርምር። The differences form a sequence: 4, 6, 8, 10. This is an arithmetic progression where each term increases by 2.

Step 3: ቀጣዩን ልዩነት እንፈልግ። Following this pattern, the next difference should be: 10+2=1210 + 2 = 12

Step 4: በተከታታይ ውስጥ ያለውን ቀጣይ ቁጥር እንፈልግ። To find the next number in the original sequence, add this difference to the last term (30): 30+12=4230 + 12 = 42

ስለዚህ, ቀጣዩ ቁጥር 42 ነው። ይህ ደግሞ አማራጭ C) ነው።

The next number in the sequence is 42\boxed{42}. The correct option is C).

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