The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A.600
B.765
C.640
D.680
Answers
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The answer is option D.680
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Concept
Arithmetic progression is defined as the sequence of the numbers which are differ by some constant. The few initial terms of the arithmetic progression is given as
a, a+d, a+2d, a+3d,......n terms, where a is the first term and d is the constant. Therefore any nth term can be calculate as,
nth term = a + (n - 1)d
Given
The first term = 5
The third term = 15
Total number of terms, n = 16
Find
We have to calculate the sum of the first 16 terms.
Solution
Since, a = 5
Therefore, 15 = 5 + (3-1)d
10 = 2d
d = 5
The formula to calculate the sum of the AP is, S = n/2[2a + (n-1)d]
Hence, S = 16/2[(2*5) + (16 - 1)*5]
S = 8[10 + 75]
S = 680
Hence the sum is 680 i.e. option D is correct.
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