What is the sum of the $12^{t h}$ to $20^{t h}$ terms (inclusive) of the arithmetic sequence $7, 12, 17, 22, . . .$ ?

516

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676

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117

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667

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Solution

The correct option is B $676$
First term $a = 7 d = 5$
We know the formula,
$S_{n} = \frac{n}{2} [2 \times a (n - 1) d]$
$S_{12} = \frac{12}{2} [2 \times 7 + (12 - 1) 5]$
$S_{12} = 414$
$S_{20} = \frac{20}{2} [2 \times 7 + (20 - 1) 5]$
$S_{20} = 1090$
Therefore the sum of the $12^{t h}$ to $20^{t h}$ terms $= 1090 - 414 = 676$

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What is the sum of the 12th to 20th terms (inclusive) of the arithmetic sequence 7,12,17,22,...?

The correct option is B 676First term a=7d=5We know the formula,Sn=n2[2×a(n−1)d]S12=122[2×7+(12−1)5]S12=414S20=202[2×7+(20−1)5]S20=1090Therefore the sum of the 12th to 20th terms =1090−414=676

What is the sum of the $12^{t h}$ to $20^{t h}$ terms (inclusive) of the arithmetic sequence $7, 12, 17, 22, . . .$ ?