Question

6. The 26 th term,11 th term and the last term of an AP are 0,3 and-1/5
respectively. Find the
common difference and the number of terms.

Answer 1

Answer:

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Step-by-step explanation:

a26 = 0 , a11 = 3 and an (last term) = -1/5 of an A.P. We know that, nth term an = a + (n – 1)d Then, a26 = a + (26 – 1)d ⇒ a + 25d = 0 …..(1) And, a11 = a + (11 – 1)d ⇒ a + 10d = 3 …… (2) Solving (1) and (2), (1) – (2) ⇒ a + 25d – (a + 10d) = 0 – 3 15d = -3 ⇒ d = -1/5 Using d in (1), we get a + 25(-1/5) = 0 a = 5 Now, given that the last term an = -1/5 ⇒ 5 + (n – 1)(-1/5) = -1/5 5 + -n/5 + 1/5 = -1/5 25 – n + 1 = -1 n = 27 Therefore, the A.P has 27 terms and its common difference is -1/5.