Mathematics

(a) Write the nth term (T_n) of an Arithmetic Progression (A.P.) consisting of all whole numbers which are divisible by 3 and 7.
(b) How many of these are two-digit numbers? Write them.
(c) Find the sum of first 10 terms of this A.P.

AP GP

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Answer

(a) A.P. = 21, 42, 63, ………

The above sequence is an A.P. with first term (a) = 21 and common difference (d) = 21.

By formula,

T_n = a + (n - 1)d

= 21 + (n - 1)21

= 21 + 21n - 21

= 21n.

Hence, the n^th term = 21n.

(b) A.P. = 21, 42, 63, 84, 105, ……..

Hence, there are four two digit numbers i.e. 21, 42, 63, 84 in the A.P.

Sum of A.P. = $\dfrac{n}{2}(a + a_n)$

$\text{Sum of first 10 terms of A.P.} = \dfrac{10}{2}(a + a_{10}) \\[1em] = 5[a + a + (n - 1)d] \\[1em] = 5[2a + (n - 1)d] \\[1em] = 5[2 \times 21 + (10 - 1) \times 21] \\[1em] = 5[42 + 9 \times 21] \\[1em] = 5[42 + 189] \\[1em] = 5 \times 231 \\[1em] = 1155.$

Hence, sum of first 10 terms of the A.P. = 1155.

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Mathematics

(a) Write the nth term (T_n) of an Arithmetic Progression (A.P.) consisting of all whole numbers which are divisible by 3 and 7.
(b) How many of these are two-digit numbers? Write them.
(c) Find the sum of first 10 terms of this A.P.

AP GP

Answer

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