Question

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of an AP


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Answer 1

Given :-

• n = 50
• a3 = 12
• l = an = 106

To find :-

• a 29

Solution :-

• an = a + ( n - 1 ) d
• 106 = a + ( 50 - 1 ) d
• 106 = a + 49d ------- (1)

For equation 2

• a3 = a + 2d
• 12 = a + 27d ------- (2)

Solving equation (1) and (2)

• 106 - 12 = a + 49d - [ a + 2d ]
• 94 = a + 49d - a - 2d
• 94 = 47d
• 94/47 = d
• 2 = d

Hence, common difference is 2

• a3 = a + 2d
• 12 = a + 2(2)
• 12 = a + 4
• 12 - 4 = a
• 8 = a

Hence, first term is 8

➡ a29 = a + 28d

➡ a29 = 8 + 28(2)

➡ a29 = 8 + 56

➡ a29 = 64

29th term of an AP is 64