The second term from beginning and end of an A.P. are 9 and 39 respectively. If the sum of its terms is 192, then the number of terms will be.
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The second term from beginning and end of an A.P. are 9 and 39 respectively. If the sum of its terms is 192, then the number of terms will be.
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Answer:
Number of terms = 8
Explanation:
Let the number of terms of A.P. be n.
First term = a and common difference = d.
Note :-
rth term from end = (n - r + 1) th term from beginning.
2nd term from end = (n - 2 + 1) = (n - 1)th term from beginning.
T_2 = a + d = 9 - - - (i)
T_(n - 1) = a + (n - 1 -1)d = 39
T_(n - 1) = a + (n - 2)d = 39 - - (ii)
S_n = (n/2)[ 2a + (n - 1)d] = 192 - - -(iii)
Now, subtracting (i) from (ii) we get,
(n - 3)d = 30 - - -(iv)
from (i), d = (9 - a)
S_n = (n/2) [ a + a + (n - 2)d + d] = 192
=> (n/2) [ a + 39 + 9 - a ] = 192
{ from results (i) and (ii) }
(n/2) (48) = 192
n = 192 / 24 = 8
Hence, the number of terms will be 8.
Explanation:
Read the source given below and answer the questions that follow:(1X4=4)
In Pakistan, General Pervez Musharraf led a military coup in October 1999. He
overthrew a democratically elected government and declared himself the ‘Chief
Executive’ of the country. Later he changed his designation to President and in
2002 held a referendum in the country that granted him a five-year extension.
Pakistani media, human rights organisations and democracy activists said that the
referendum was based on malpractices and fraud. In August 2002 he issued
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