Show that a1, a2 … , an , … form an AP where an is defined as below an = 3 + 4n Also find the sum of the first 15 terms in each case. - Mathematics

Sum

Show that a1, a… , an , … form an AP where an is defined as below

an = 3 + 4n

Also find the sum of the first 15 terms.

Solution

an = 3 + 4n

a1 = 3 + 4(1) = 7

a2 = 3 + 4(2) = 3 + 8 = 11

a3 = 3 + 4(3) = 3 + 12 = 15

a4 = 3 + 4(4) = 3 + 16 = 19

It can be observed that

a2 − a1 = 11 − 7 = 4

a3 − a2 = 15 − 11 = 4

a4 − a3 = 19 − 15 = 4

i.e., ak + 1 − ak is same every time. Therefore, this is an AP with common difference as 4 and first term as 7.

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

S_15 = 15/2 [2(7) + (15 - 1) × 4]

= 15/2 [(14) + 56]

= 15/2 (70)

= 15 × 35

= 525

Concept: Sum of First n Terms of an AP
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APPEARS IN

NCERT Class 10 Maths
Chapter 5 Arithmetic Progressions
Exercise 5.3 | Q 10.1 | Page 113