# The ratio of third and tenth term of an arithmetic progression is 9 : 10. If the sum of first three terms is 930, then find the fifth term of AP.

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The ratio of third and tenth term of an arithmetic progression is 9 : 10. If the sum of first three terms is 930, then find the fifth term of AP.
1. 305
2. 275
3. 325
4. 340
5. 295

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Correct Answer - Option 3 : 325

Calculations:

Ratio of third and tenth term = 9 : 10

Sum of first 3 terms = 930

Now, (a + 2d)/(a + 9d) = 9/10

⇒ 10 × (a + 2d) = 9 × (a + 9d)

⇒ 10a + 20d = 9a + 81d

⇒ (10 - 9)a = (81 - 20)d

⇒ a = 61d      ----(1)

Also, (3/2) × (2a + (3 - 1) × d) = 930

⇒ 2(a + d) = 930 × (2/3) = 310

⇒ a + d = 310

Substituting a from (1) in this equation, we get

(61 + 1)d = 310

⇒ d = 310/62 = 5

a = 61 × 5 = 305

Fifth term of AP = (a + 4d)

⇒ (a + 4d) = 305 + 4 × 5 = 325

∴ The fifth term of AP is 325.

In an AP,

an = a + (n - 1) × d

Sn = (n/2) × (2a + (n - 1) × d)

where, a → First term, d → Common difference,

n → Number of terms