In an A.P., the 5th and 9th terms are 4 and -12 respectively. Find the: (a) first term (b) common difference (c) sum of the first 20 terms.

If first term is a and common difference is d of the A.P. By formula, nth term = an = a + (n - 1)d Given, ⇒ 5th term = 4 ⇒ a5 = 4 ⇒ a + (5 - 1)d = 4 ⇒ a + 4d = 4 .........(1) ⇒ 9th term = -12 ⇒ a9 = -12 ⇒ a + (9 - 1)d = -12 ⇒ a + 8d = -12 .........(2) Subtracting equation (1) from (2), we get : ⇒ (a + 8d) - (a + 4d) = -12 - 4 ⇒ a - a + 8d - 4d = -16 ⇒ 4d = -16 ⇒ d = ⇒ d = -4. Substituting value of d in equation (1), we get : ⇒ a + 4d = 4 ⇒ a + 4(-4) = 4 ⇒ a - 16 = 4 ⇒ a = 4 + 16 = 20. (a) Hence, first term of A.P. = 20. (b) Common difference of A.P. = -4. (c) By formula, Sum of n terms of A.P. = Sum of first 20 terms of A.P. = Hence, sum of 20 terms of A.P. = -360.

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Find the sum of first 22 terms of an A.P. in which d = 7 and a₂₂ is 149.

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Mathematics

In an A.P., the 5^th and 9^th terms are 4 and -12 respectively. Find the:
(a) first term
(b) common difference
(c) sum of the first 20 terms.

A.P.

Related Questions

How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78 ? Explain the double answer.

Find the sum of first 22 terms of an A.P. in which d = 7 and a₂₂ is 149.

Find the sum of first 51 terms of the A.P. whose second and third terms are 14 and 18 respectively.

The 4th term of an A.P. is 22 and 15th term is 66. Find the first term and the common difference. Hence, find the sum of first 8 terms of the A.P.

Mathematics

In an A.P., the 5th and 9th terms are 4 and -12 respectively. Find the:(a) first term(b) common difference(c) sum of the first 20 terms.

A.P.

Related Questions

How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78 ? Explain the double answer.

Find the sum of first 22 terms of an A.P. in which d = 7 and a22 is 149.

Find the sum of first 51 terms of the A.P. whose second and third terms are 14 and 18 respectively.

The 4th term of an A.P. is 22 and 15th term is 66. Find the first term and the common difference. Hence, find the sum of first 8 terms of the A.P.

In an A.P., the 5^th and 9^th terms are 4 and -12 respectively. Find the:
(a) first term
(b) common difference
(c) sum of the first 20 terms.

Find the sum of first 22 terms of an A.P. in which d = 7 and a₂₂ is 149.