Saved Bookmarks
| 1. |
find the m th term of an arithmatic progression whose 12 th term exceeds the 5 th term by 14 and the sum of both term is 36. |
|
Answer» Step-by-step explanation:The 12th term of the A.P exceeds the 5th term by 14Sum of both the term is 36The MTH term➢ First we have to find the COMMON difference and first term of the A.P➢ The 12 th term of an A.P is given by, a₁₂ = a₁ + 11d➢ The 5th term of an A.P is given by, a₅ = a₁ + 4d---------(1)➢ By given, a₁₂ = a₅ + 14➢ Substitute the value of a₅ from equation 1➢ HENCE, a₁ + 11d = a₁ + 4d + 14➢ Cancelling a₁ on both sides, 11d = 4d + 14 11d - 4d = 14 7d = 14 d = 14/7 d = 2➢ Hence common difference of the A.P is 2.➢ Now also by given, a₅ + a₁₂ = 36 a₁ + 4d + a₁ + 11d = 36 2a₁ + 15d = 36➢ Substitute the value of d, 2a₁ + 15 × 2 = 36 2a₁ = 6 a₁ = 3➢ Hence the first term of the A.P is 3.➢ Now the mth term of the A.P is given by, ➢ Substitute the values, ➢ Hence the mth term of the A.P is 2m + 1 |
|