Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120? - Mathematics

MCQ

In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

• 6

• 7

• 8

• 9

#### Solution

8

Explanation;

Here a = 1, d = 4, Sn = 120

Sn = "n"/2 [2"a" + ("n" - 1)"d"]

120 = "n"/2 [2 + ("n" - 1)4]

= "n"/2 [2 + 4"n" - 4]

= "n"/2 [4"n" - 2]

= "n"/2 xx 2 (2"n" - 1)

120 = 2n2 – n

∴ 2n2 – n – 120 = 0

⇒ 2n2 – 16n + 15n – 120 = 0

2n(n – 8) + 15 (n – 8) = 0

⇒ (n – 8) (2n + 15) = 0

n = 8 or n = (-15)/2 ...(omitted)

∴ n = 8

Concept: Series
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#### APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 2 Numbers and Sequences
Exercise 2.10 | Q 11 | Page 82