Question

find middle term of ap 6,13,20,...,216

Answer 1

Hey there !!


➡ Given :-

→ a$\tiny 1$ = 6.

→ a$\tiny 2$ = 13.

→ Then, d = a$\tiny 2$ - a$\tiny 1$ .

=> d = 13 - 6 = 7.

→ a$\tiny n$ = 216.


➡ To find :-

→ Middle term of AP.


➡ Solution :-


▶ Let the given AP contain n terms .

▶ Then, nth term is given by :-


→ a$\tiny n$ = a + ( n - 1 )d.

=> 216 = 6 + ( n - 1 ) 7.

=> 216 - 6 = 7n - 7.

=> 210 + 7 = 7n.

=> 7n = 217.

=> n = 217/7.

=> n = 31.

▶ Thus, the given AP contains 23 terms.

→ its middle term = $\frac{1}{2}$ ( n + 1 )th term .

= $\frac{1}{2}$ ( 31 + 1 )th term .

= $\frac{1}{2}$ (32) th term .

= 16th term.


▶ So, middle term = a$\tiny 16$ .

=> a$\tiny 16$ = a + ( n - 1 ) d.

= 6 + ( 16 - 1 ) × 7.

= 6 + 15 × 7.

= 6 + 105.

$\huge \boxed{ \bf = 111 . }$


✔✔ Hence , it is solved ✅✅.

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THANKS


#BeBrainly.