Question

In an A.P. if a 11 = 7 and a7 = 11 then, d = ?
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Answer 1

Answer:

Step-by-step explanation:

irst we must find the 7th and 11th terms of the A.P and then equate them. In an A.P., the nth term is given as, Tn=a+(n−1)d, where a is the first term and d is a common difference.

Complete step-by-step answer:

Given, 7 times the 7th term is equal to 11 times the 11th term

⇒7×T7=11×T11

Let the first term be a and common difference be d.

Since, Tn=a+(n−1)d , where a is the first term and d is the common difference.

⇒7(a+6d)=11(a+10d)⇒7a+42d=11a+110d⇒−4a=68d⇒a=−17d

Now, we have to find the value of the 18th term

⇒T18=a+(n−1)d⇒T18=a+(18−1)d⇒T18=a+17d

Putting, a =-17d in the above equation

⇒T18=−17d+17d=0

Therefore, the 18th term is 0.

Note: Arithmetic Mean is always greater than or equal to Geometric mean. Also remember that arithmetic mean multiplied by harmonic mean will give a square of geometric mean as the result.

A.M×H.M=G.M2