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प्रश्न
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
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उत्तर
Let common difference be d.
a = 3
Sum of first n terms of an A.P. = `n/2(a + 1)`
Given,
The sum of the first 8 terms is twice the sum of the first 5 terms.
∴ `8/2(a + a_8) = 2 xx 5/2(a + a_5)`
⇒ 4[a + a + (8 − 1)d] = 5[a + a + (5 − 1)d]
⇒ 4[2a + 7d] = 5[2a + 4d]
⇒ 4[2 × 3 + 7d] = 5[2 × 3 + 4d]
⇒ 4[6 + 7d] = 5[6 + 4d]
⇒ 24 + 28d = 30 + 20d
⇒ 28d − 20d = 30 − 24
⇒ 8d = 6
⇒ d = `6/8`
⇒ d = `3/4`
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