Question 12 If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be
A) 7 B) 11 C) 18 D) 0
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Solution
According to the question, 7a7=11a11 ⇒7[a+(7−1)d]=11[a+(11−1)d][∵an=a+(n−1)d] ⇒7(a+6d)=11(a+10d) ⇒7a+42d=11a+110d ⇒4a+68d=0 ⇒2(2a+34d)=0[∵2≠0] ⇒2a+34d=0 ⇒a+17d=0⋯(i) ∴ 18th term of the AP, a18=a+(18−1)d =a+17d=0[fromeq.(i)]