# Show that a1, a2 … , an , … form an AP where an is defined as below an = 9 − 5n 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 = 9 − 5n

Also find the sum of the first 15 terms.

#### Solution

an = 9 − 5n

a1 = 9 − 5 × 1 = 9 − 5 = 4

a2 = 9 − 5 × 2 = 9 − 10 = −1

a3 = 9 − 5 × 3 = 9 − 15 = −6

a4 = 9 − 5 × 4 = 9 − 20 = −11

It can be observed that

a2 − a1 = − 1 − 4 = −5

a3 − a2 = − 6 − (−1) = −5

a4 − a3 = − 11 − (−6) = −5

i.e., ak + 1 − ak is same every time. Therefore, this is an A.P. with common difference as −5 and first term as 4.

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

S_15 = 15/2 [2(4) + (15 - 1) (-5)]

= 15/2 [8 + 14(-5)]

= 15/2 (8 - 70)

= 15/2 (-62)

= 15(-31)

= -465

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 10.2 | Page 113