An Arithmetic Progression (A.P.) consists of all whole numbers which are divisible by 3 and 5.
(a) Write its first term and the common difference.
(b) Find the 10th term of the A.P.
(c) Find the sum of the first 10 terms of the A.P.
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(a) Given,
The A.P. consists of all whole numbers which are divisible by 3 and 5.
A number which is divisible by both 3 and 5 is divisible by their L.C.M.
L.C.M. of 3 and 5 = 15
Thus, the A.P. is 15, 30, 45, 60, ......
First term (a) = 15
Common difference (d) = 30 − 15 = 15.
Hence, first term = 15 and common difference = 15.
(b) By formula,
tn = a + (n - 1)d
Substituting values, we get :
⇒ t10 = 15 + (10 − 1) × 15
⇒ t10 = 15 + 9 × 15
⇒ t10 = 15 + 135
⇒ t10 = 150.
Hence, the 10th term of the A.P. = 150.
(c) By formula,
$S_n = \frac{n}{2}[2a + (n - 1)d]$
Substituting values, we get :
⇒ S10 = $\frac{10}{2}[2 \times 15 + (10 - 1) \times 15]$
⇒ S10 = 5[30 + 9 × 15]
⇒ S10 = 5[30 + 135]
⇒ S10 = 5 × 165
⇒ S10 = 825.
Hence, the sum of the first 10 terms of the A.P. = 825.