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.

Given, a 4 = 22 and a 15 = 66. By formula, a n = a + (n - 1)d ⇒ a 4 = a + (4 - 1)d ⇒ 22 = a + 3d ⇒ a = 22 - 3d (Eq 1) ⇒ a 15 = a + (15 - 1)d ⇒ 66 = a + 14d Putting value of a from Eq 1 in above equation ⇒ 66 = 22 - 3d + 14d ⇒ 66 = 22 + 11d ⇒ 11d = 66 - 22 ⇒ 11d = 44 ⇒ d = 4. Putting value of d in Eq 1, ⇒ a = 22 - 3(4) ⇒ a = 22 - 12 ⇒ a = 10. By formula S n = ⇒ S 8 = ⇒ S 8 = 4[20 + 28] ⇒ S 8 = 4 × 48 ⇒ S 8 = 192. Hence, first term = a = 10, common difference = d = 4 and sum of first 8 terms = S 8 = 192.

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Mathematics

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.

AP GP

Related Questions

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

If the sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

Show that a₁, a₂, a₃, ….. form an A.P. where a_n is defined as a_n = 3 + 4n. Also find the sum of first 15 terms.

In an A.P., the fourth and sixth terms are 8 and 14 respectively. Find the :
(i) first term
(ii) common difference
(iii) sum of first 20 terms

Mathematics

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.

AP GP

Related Questions

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

If the sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

Show that a1, a2, a3, ….. form an A.P. where an is defined as an = 3 + 4n. Also find the sum of first 15 terms.

In an A.P., the fourth and sixth terms are 8 and 14 respectively. Find the :(i) first term(ii) common difference(iii) sum of first 20 terms

Show that a₁, a₂, a₃, ….. form an A.P. where a_n is defined as a_n = 3 + 4n. Also find the sum of first 15 terms.

In an A.P., the fourth and sixth terms are 8 and 14 respectively. Find the :
(i) first term
(ii) common difference
(iii) sum of first 20 terms