Question

Find the first term and the common difference of the A.P. when

its 5th and 10th terms are 86 and 146 respectively?
​

Answer 1

★ Given:

• Fifth term = a₅ = 86
• Tenth term = a₁₀ = 146

✩ To find:

1. First term = a
2. Common Difference = d

Method:

☞ aₙ = a + (n - 1)d

➟ a₅ = a + (5 - 1)d

86 = a + 4d       ⟶ ⟶ ⟶ [Equation ❶]

Similarly,

➨ aₙ = a + (n - 1)d

➳ a₁₀ = a + (10 - 1)d

⇨146 = a + 9d       ⟶ ⟶ ⟶ [Equation ❷]

(Equation ②) - (Equation ①)

                  a + 9d = 146

            {-}  a + 4d = 86  

                         5d = 60

⇒ d = 60 ÷ 5

∴ d = 12

Substitute value of d in any one of the equations to find the value of a

Here we have substituted in Equation 1.

a + 4d = 86

⇒ a + 4(12) = 86

⇒ a + 48 = 86

⇒ a = 86 - 48

∴ a = 38

The values of

• First term = 38
• Common Difference = 12