Question : If 7 times the 7th term of an arithmetic progression (A.P.) is equal to 11 times its 11th term, then the 18th term of the A.P. will be:
Option 1: 1
Option 2: 0
Option 3: 2
Option 4: –1
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Correct Answer: 0
Solution :
Given: 7 times the 7
th
term of AP = 11 times its 11
th
term
Formula for n
th
term $⇒a+(n-1)d$
where $a$ = 1
st
term, $d$ = common difference and $n$ = number of terms
⇒ $7 × a_7 = 11 × a_{11}$
$⇒7[a+(7-1)d]=11[a+(11-1)d]$
$⇒7a+42d=11a+110d$
$⇒11a-7a+110d-42d=0$
$⇒4a+68d=0$
$⇒4(a+17d)=0$
$⇒a+17d=0$ ------------------------------(1)
Similarly, $a_{18}= [a +(18-1)d] = a+17d$
By using equation (1) we get,
⇒ $a_{18}= 0$
So, the 18
th
term is 0.
Hence, the correct answer is 0.
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