The sequence a1, a2, a3, ...... a98 satisfies the relation an+1 = a + 1 for n = 1, 2, 3,......97 and
has the sum equal to 4949, then, evaluate a2+a4+a6.......a98
Answers
Answer:
2499
Step-by-step explanation:
The sequence a1, a2, a3, ...... a98 satisfies the relation an+1 = a + 1 for n = 1, 2, 3,......97 and
has the sum equal to 4949, then, evaluate a2+a4+a6.......a98
a₁ = a
a₂ = a + 1
a₃ = a + 2
.
.
a₉₇ = a + 96
a₉₈ = a + 97
a₁ + a₂ + a₃ +.........................................+ a₉₇ + a₉₈ = 4949
=> a + a + 1 + a +2 +.............................+ a + 96 + a + 97 = 4949
=> 98a + (1 + 2 + 3 +.......................+ 96 + 97) = 4949
=> 98a + 97(98)/2 = 4949
=> 98a + 97(49) = 4949
=> 2a + 97 = 101
=> 2a = 4
=> a = 2
a₂ + a₄ + a₆ +.........................................+ a₉₆ + a₉₈
= a + 1 + a + 3 + a + 5 + ...................+ a + 95 + a + 97
= 49a + (1 + 3 + 5 +....................95 + 97)
= 49 *2 + (49/2)(1 + 97)
= 98 + 2401
= 2499
Step-by-step explanation:
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