The sum of the first q terms of an AP (arithmetic progression) is 162. The ratio of its 6th term and the 13th term is 1:2. Find the 1st and the 15th term of the AP.
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Let first term of AP is a And Common difference is d.
Given:
a6=a+5d
a13=a+12d
a6/a13=1/2
=>a+5d/a+12d=1/2
=>2a+10d=a+12d
=>a=2d
Also,
S9=9/2×[2a+(9−1)d]
=>162=9/2×(2a+8d)
=>36=[4d+8d]
=>d=3
Then a = 6
a15=6+14×3=48
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