Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24^th term.

Solution

Given: S₂₀ = -240 and a = 7

Consider, S₂₀ = -240

$S_{n} = \frac{n}{2} [2 a + (n - 1) d] \Rightarrow - 240 = \frac{20}{2} [2 x 7 + (20 - 1) d] \Rightarrow - 240 = 10 (14 + 19 d) \Rightarrow - 24 = 14 + 19 d \Rightarrow - 24 - 14 = 19 d \Rightarrow 19 d = - 38 \Rightarrow d = - 2$

Now, a₂₄ = a + 23d

= 7 + 23 x (-2)

= -39

Hence, a₂₄ = -39

Some More Questions From Arithmetic Progressions Chapter

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Arithmetic Progressions

Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24^th term.

Some More Questions From Arithmetic Progressions Chapter

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25

For the following APs, write the first term and the common difference
3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference
– 5, – 1, 3, 7, . . .

For the following APs, write the first term and the common difference
0.6, 1.7, 2.8, 3.9, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
– 1.2, – 3.2, – 5.2, – 7.2, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
–10, –6, –2, 2, ....

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For Daily Free Study Material Join wiredfaculty

Arithmetic Progressions

Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24th term.

Some More Questions From Arithmetic Progressions Chapter

Write first four terms of the AP, when the first term a and the common difference d are given as follows:a = – 1.25, d = – 0.25

For the following APs, write the first term and the common difference3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference– 5, – 1, 3, 7, . . .

For the following APs, write the first term and the common difference0.6, 1.7, 2.8, 3.9, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.– 1.2, – 3.2, – 5.2, – 7.2, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. –10, –6, –2, 2, ....

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24^th term.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25

For the following APs, write the first term and the common difference
3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference
– 5, – 1, 3, 7, . . .

For the following APs, write the first term and the common difference
0.6, 1.7, 2.8, 3.9, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
– 1.2, – 3.2, – 5.2, – 7.2, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
–10, –6, –2, 2, ....