Question

Find the number of terms of the AP - 12, - 9, - 6,.....,21. If 1 is added to each term of this AP then find the sum of all terms of the AP thus obtained.

Answer 1

I hope this is the right answer

Answer 2

Hey there !!


➡ Given :-

→ a$\tiny 1$ = -12.

→ a$\tiny 2$ = -9.

Then, d = a$\tiny 2$ - a$\tiny 1$ .

=> d = -9 - (-12) .

=> d = -9 + 12 = 3.

→ a$\tiny n$ = 21.


➡ To find :-

→ S$\tiny n$ .


➡ Solution :-


▶ Using Identity :-

→ a$\tiny n$ = a + ( n - 1 )d.

=> 21 = -12 + ( n - 1 ) × 3.

=> 21 + 12 = 3n - 3.

=> 33 + 3 = 3n.

=> n = 36/3.

=> n = 12.

▶ Now,

A/Q,

→ 1 is added to each AP.

Then,

→ a$\tiny 1$ = -12 + 1 = -11.

→ a$\tiny n$ = 21 + 1 = 22.


▶ Now,

→ Using Identity :-

→ S$\tiny n$ = n/2 ( a + a$\tiny n$ ).

=> S$\tiny 12$ = 12/2 ( -11 + 22 ).

=> S$\tiny 12$ = 6 × 11.

$\huge \boxed{ => S \tiny 12 \large = 66. }$


✔✔ Hence, it is solved ✅✅.

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THANKS

#BeBrainly.