the sum of the fourth and twelfth term of an arithmetic progression is 20. what is the sum of the first 16 terms of the arithmetic progression?  Options.
A) 300  B) 120  C) 150  D) 160  E) 270
<gadget id="calculator">20 * 16</gadget>
<output>320</output>

<gadget id="calculator">320 / 2</gadget>
<output>160</output>

<result>D</result>
the sum of the fourth and twelfth term of an arithmetic progression is 20. what is the sum of the first 16 terms of the arithmetic progression?
divide(multiply(20, 16), const_2)
"n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 16 . . . we get 15 / 2 [ 2 a + 14 d ] = 16 [ a + 7 d ] = 16 * 10 = 160 . . . answer is d . . ."