sum of first 30 terms of an ap is 1920 fourth term 18.find first term and common difference
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Answer:
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Answer:-
Given:
Sum of first 30 terms of an AP – S(30) = 1920
Fourth term – a(4) = 18
We know that,
Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]
Hence,
→ 1920 = 30/2 * [ 2a + (30 - 1)d ]
→ 1920 * 2/30 = 2a + 29d
→ 128 = 2a + 29d -- equation (1).
We know,
nth term of an AP – a(n) = a + (n - 1)d
Therefore,
→ 18 = a + (4 - 1)d
→ 18 = a + 3d -- equation (2)
Multiply equation (2) by 2 and subtract equation (2) from (1).
→ 128 - 2 (18) = 2a + 29d - 2 ( a + 3d )
→ 128 - 36 = 2a + 29d - 2a - 6d
→ 92 = 23d
→ 92/23 = d
→ 4 = d
Substitute the value of d in equation (1).
→ 2a + 29 * 4 = 128
→ 2a + 116 = 128
→ 2a = 128 - 116
→ 2a = 12
→ a = 12/2
→ a = 6
Therefore, the first term and common difference of the given AP are 6 , 4.