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Answer 1

4. 5th term of AP = 17

We know that :- Tn = a + (n-1)d

where :-

• a = first term
• n = number of terms
• d = common difference
• Tn = nth term

⟹ T5 = a + (5-1)d

⟹ 17 = a + 4d

⟹ 17 - 4d = a .... [1]

10th term of AP = 32

We know that :- Tn = a + (n-1)d

⟹ T10 = a + (10-1)d

⟹ 32 = a + 9d

⟹ 32 - 9d = a .... [2]

(a) Now to find out common difference :-

compare [1] and [2]

⟹ 17 - 4d = 32 - 9d

⟹ 9d - 4d = 32 - 17

⟹ 5d = 15

⟹ d = 15/5

⟹ d = 3 ( d = common difference)

(b) Now to find first term :-

put d = 3 in 17 - 4d = a

⟹ a = 17 - 4d

⟹ a = 17 - 4(3)

⟹ a = 17 - 12

⟹ a = 5 ( a = first term)

(c) Now we have to find position of 92 in the sequence :-

use the formula :- Tn = a + (n-1)d

put :-

• Tn = 92
• a = 5
• d = 3

⟹ Tn = a + (n-1)d

⟹ 92 = 5 + (n-1)3

⟹ 92 = 5 + (n-1)3

⟹ 92-5 = (n-1)3

⟹ 87 = (n-1)3

⟹ 87/3 = (n-1)

⟹ 29 = n-1

⟹ 29+1 = n

⟹ 30 = n

Therefore 92 is at 30th position in this sequence.

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Learn more :

1. Tn = a+(n-1)d

2. Sn = n/2[2a+(n-1)d]

3. Sn = n/2(a+l)

where :-

• a = first term
• n = number of terms
• d = common difference
• Tn = nth term
• l = last term

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