Question

(ii) Find the AP whose Ist term is 100 and the sum of the first six terms is 5 times
the sum of the next six terms.​

Answer 1

Answer:

$Here a=100</p><p></p><p></p><p>Let difference is d.</p><p>⇒a1+a2+a3+a4+a5+a6=5(a7+a8+a9+a10+a11+a12)</p><p></p><p>So by the formula, Sn=2n(a+l), where a &l are the first and last term of an AP, we have</p><p>6(2a1+a6)=5×6(2a7+a12)</p><p></p><p>⇒a1+a6=5(a7+a12)</p><p></p><p>⇒a+a+5d=5(a+6d+a+11d)</p><p></p><p>⇒2a+5d=10a+85d</p><p></p><p>⇒80d=−8a</p><p></p><p>⇒d=10−a⇒10−100⇒−10</p><p></p><p>$