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If 15 times of the 21st term of an A.P. is equal to 20 times of 31st term, then, find the 61st term of the A.P.?
1. 1
2. -1
3. 2
4. 0

1 Answer

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Correct Answer - Option 4 : 0

Given:

15T21 = 20T31

Formula used:

Tn = a + (n – 1) d

Where, a = first term, n = the number of term and d = common difference

Calculation:

T21 = a + (21 – 1) d

⇒ T21 = a + 20d      ----- (1)

T31 = a + (31 – 1) d

⇒ T31 = a + 30d      ----- (2)

According to question –

⇒ 15 × (a + 20d) = 20 × (a + 30d)

⇒ 15a + 300d = 20a + 600d

⇒ 5a + 300d = 0

⇒ a + 60d = 0      ----- (3)

From equation (3), we have –

∴ T61 = a + (61 – 1) d

⇒ T61 = a + 60d = 0

∴ 61st term of the A.P. is zero.

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