QQuestion
The 4th and the 7th terms of an A.P. are 60 and 114 respectively. Find:
(a) the first term and the common difference.
(b) the sum of the first 10 terms.
ICSEClass XMathematicsArithmetic And Geometric Progression04 Mark2026 Moderate
✓Answer
Let the first term be a and the common difference be d.
The nth term of an A.P. is Tₙ = a + (n − 1)d.
For the 4th term:
a + 3d = 60 …(1)
For the 7th term:
a + 6d = 114 …(2)
Subtracting (1) from (2):
3d = 54
⇒ d = 18
Substituting d = 18 in (1):
a + 3(18) = 60
⇒ a + 54 = 60
⇒ a = 6
Therefore, the first term is 6 and the common difference is 18.
Now, Sₙ = \frac{\mathrm{n}}{2}[2\mathrm{a}+(\mathrm{n}-1)\mathrm{d}]
S₁₀ = \frac{10}{2}[2(6)+(10-1)(18)]
⇒ S₁₀ = 5[12 + 162]
⇒ S₁₀ = 5 × 174
⇒ S₁₀ = 870
Therefore, the sum of the first 10 terms is 870.
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