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

Given, a 4 = 8 and a 6 = 14. By formula, a n = a + (n - 1)d ⇒ a 4 = a + (4 - 1)d ⇒ 8 = a + 3d ⇒ a = 8 - 3d (Eq 1) ⇒ a 6 = a + (6 - 1)d ⇒ 14 = a + 5d Putting value of a from Eq 1 in above equation ⇒ 14 = 8 - 3d + 5d ⇒ 14 = 8 + 2d ⇒ 2d = 14 - 8 ⇒ 2d = 6 ⇒ d = 3. Putting value of d in Eq 1, ⇒ a = 8 - 3(3) ⇒ a = 8 - 9 ⇒ a = -1. (i) Hence, the first term of the A.P. is -1. (ii) Hence, the common difference of the A.P. = 3. (iii) By formula S n = ⇒ S 20 = ⇒ S 20 = 10[-2 + 57] ⇒ S 20 = 10 × 55 ⇒ S 20 = 550. Hence, the sum of first 20 terms of the A.P. is 550.

If the 4th, 10th and 16th terms of a G.P. are x, y and z respectively, prove that x, y, z are in G.P.

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15, 30, 60, 120 …… are in G.P. (Geometric Progression).
(a) Find the nth term of this G.P. in terms of n.
(b) How many terms of the above G.P. will give the sum 945 ?

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The roots of the equation (q - r)x² + (r - p)x + (p - q) = 0 are equal.
Prove that : 2q = p + r, that is, p, q and r are in A.P.

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Mathematics

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

AP GP

Related Questions

If the 4th, 10th and 16th terms of a G.P. are x, y and z respectively, prove that x, y, z are in G.P.

15, 30, 60, 120 …… are in G.P. (Geometric Progression).
(a) Find the nth term of this G.P. in terms of n.
(b) How many terms of the above G.P. will give the sum 945 ?

The roots of the equation (q - r)x² + (r - p)x + (p - q) = 0 are equal.
Prove that : 2q = p + r, that is, p, q and r are in A.P.

Mathematics

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

AP GP

Related Questions

If the 4th, 10th and 16th terms of a G.P. are x, y and z respectively, prove that x, y, z are in G.P.

15, 30, 60, 120 …… are in G.P. (Geometric Progression).(a) Find the nth term of this G.P. in terms of n.(b) How many terms of the above G.P. will give the sum 945 ?

The roots of the equation (q - r)x2 + (r - p)x + (p - q) = 0 are equal.Prove that : 2q = p + r, that is, p, q and r are in A.P.

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

15, 30, 60, 120 …… are in G.P. (Geometric Progression).
(a) Find the nth term of this G.P. in terms of n.
(b) How many terms of the above G.P. will give the sum 945 ?

The roots of the equation (q - r)x² + (r - p)x + (p - q) = 0 are equal.
Prove that : 2q = p + r, that is, p, q and r are in A.P.