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If a = 18 and d = 30, then sum of first 6 terms of the A.P. is?
555
558
559
561
558
Calculate the average of the first and last term: last=a+(nтИТ1)d=18+5(30)=168. Then Sum=n├Ч2a+lтАЛ=6├Ч218+168тАЛ=3├Ч186=558.
First term a = 18, common difference d = 30, and number of terms n = 6.
SnтАЛ=2nтАЛ[2a+(nтИТ1)d]
Calculate the average of the first and last term: last=a+(nтИТ1)d=18+5(30)=168. Then Sum=n├Ч2a+lтАЛ=6├Ч218+168тАЛ=3├Ч186=558.
Many students forget the (nтИТ1) in the arithmetic progression formula or mistakenly use n instead of nтИТ1 for the common difference component.
Identify parameters
Identify the given values for the arithmetic progression: the first term a=18, the common difference d=30, and the number of terms n=6.
a=18,d=30,n=6
Apply the sum formula
Substitute the given values into the formula for the sum of n terms of an AP: SnтАЛ=2nтАЛ[2a+(nтИТ1)d].
S6тАЛ=26тАЛ[2(18)+(6тИТ1)30]
Perform calculation
Simplify the expression inside the brackets: 2(18)=36 and (5)(30)=150. Adding these gives 186. Multiply by 3 to find the final sum.
S6тАЛ=3├Ч[36+150]=3├Ч186=558
B is correct because the sum of the first 6 terms calculated using the arithmetic progression formula results in 558.
Understanding the sum of an AP is essentially finding the sum of a linear sequence, which is a foundational concept for calculus sequences and series.
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