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12345512
@12345512
August 2021
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the sum of the third and the seventh term of an ap is 6 and their product is 8 find the sum of first 16 term of the AP.
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tr467
▶ Question :-
→ The sum of the third and the seventh term of an ap is 6 and their product is 8 find the sum of first 16 term of the AP.
▶ Answer :-
→ 76 and 20 .
▶ Step-by-step explanation :-
➡ Given :-
→
→
➡ To find :-
→ The sum of first 16th term of an AP .
Here,
a = first term
n = no. of terms
d = common difference
We have,
°•°
==> a + ( 3 - 1 )d + a( 7 - 1 )d = 6 .
==> 2a + 8d = 6.
==> a + 4d = 3 .
•°• a = 3 - 4d .
▶ And,
°•°
==> (a + 2d)(a + 6d) = 8 .
==> (3 - 2d)( 3 + 2d) = 8 { putting a = 3 - 2d, we get }
==> 9 - 4d² = 8 .
==> d = ± 1/2 . [ +1/2 and - 1/2 ]
So, when d = +1/2 then a = 3 - 2 = 1 and when d = -1/2, then a = 3 + 2 = 5 .
▶ So, using formula
→
→ When, d = +1/2 .
Then,
→ Similarly, when d = -1/2 .
Then,
✔✔ Hence, it is solved ✅✅.
2 votes
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Answers & Comments
→ The sum of the third and the seventh term of an ap is 6 and their product is 8 find the sum of first 16 term of the AP.
▶ Answer :-
→ 76 and 20 .
▶ Step-by-step explanation :-
➡ Given :-
→
→
➡ To find :-
→ The sum of first 16th term of an AP .
Here,
a = first term
n = no. of terms
d = common difference
We have,
°•°
==> a + ( 3 - 1 )d + a( 7 - 1 )d = 6 .
==> 2a + 8d = 6.
==> a + 4d = 3 .
•°• a = 3 - 4d .
▶ And,
°•°
==> (a + 2d)(a + 6d) = 8 .
==> (3 - 2d)( 3 + 2d) = 8 { putting a = 3 - 2d, we get }
==> 9 - 4d² = 8 .
==> d = ± 1/2 . [ +1/2 and - 1/2 ]
So, when d = +1/2 then a = 3 - 2 = 1 and when d = -1/2, then a = 3 + 2 = 5 .
▶ So, using formula
→
→ When, d = +1/2 .
Then,
→ Similarly, when d = -1/2 .
Then,
✔✔ Hence, it is solved ✅✅.