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The middle term(s) of the following series 2 + 4 + 6 + ... + 198 is
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- 98
- 96
- 94
- 100
- 98
Correct Option: D
Given , 2 + 4 + 6 + 8 + ...... + 198 = 2 (1 + 2 + 3 + ....... + 99 )
∴ Number of terms = 99
Middle term = | = 50th term | |
2 |
Middle term = 100
Second method to find the required answer with the help of formula :
It is an arithmetic series.
a = 2, an = 198, d = common difference = 2
Number of terms = n
∴ an = a + (n – 1)d
⇒ 198 = 2 + (n – 1)2
⇒ (n – 1)2 = 198 – 2 = 196
⇒ n – 1 = | = 98 | |
2 |
⇒ n = 99
Middle term = | = 50th term | |
2 |
∴ a50 = 2 + (50 – 1)2
a50 = 2 + 98 = 100