The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.
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The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.
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HELLO DEAR,
let first term be a.
common difference be d.
according to question,
CASE- 1
CASE-2
[put in ----( 1 )]
we get,
2( 1 ) + 7d = 30
7d = 30 - 2
7d = 28
d = 28/7
d = 4
thus, a = 1 , d = 4
so, the arithmetic series is; 1 , (1 + 4) , (1 + 2*4) , (1 + 3*4) , (1 + 4*4).....
1 , 5 , 9 , 13 , 17.......
I HOPE IT'S HELP YOU DEAR,
THANKS
➡️ let the first term be x
➡️ Difference be d
In Case 1
a2 + a7 = 30
=> {a + ( 2 - 1 ) d } + { a + 7 - 1 ) d } = 30
➡️ 2a + 7d = 30 - - - - - - - ( 1 )
Now,
In case 2
a15 = 2a8 - 1
➡️ {a + ( 15 - 1 ) d = 2 { a + ( 8 - 1 ) d} - 1
=> 2a - a + 14d - 14d - 1 = 0
Therefore,
Value of a = 1
Put this value in equation ( 1 )
We get,
a(1) + 7d = 30
7d = 28
d = 28 / 7
d = 4
Therefore,
a =1 and d = 4
So the arithmetic series
1, (1+4), ( 1+2×4), (1 +3×4),(1+4×4)......
1,5,9,13,17 ✔️✔️✔️✔️
HOPE IT WILL HELP YOU
BE BRAINLY