Question

if for an a.p.s 15= 147 and s 14 = 123 find t 15
​

Answer 1

$\textbf{Given:}$

$\textsf{In an A.P,}$

$\mathsf{S_{15}=147,\;\;S_{14}=123}$

$\textbf{To find:}$

$\mathsf{t_{15}}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{S_{15}=147}$

$\implies\mathsf{t_1+t_2+.\;.\;.\;.\;.\;.\;.+t_{14}+t_{15}=147}$

$\implies\mathsf{(t_1+t_2+.\;.\;.\;.\;.\;.\;.+t_{14})+t_{15}=147}$

$\implies\mathsf{(Sum\;of\;first\;14\;terms\;of\;the\;A.P)+t_{15}=147}$

$\implies\mathsf{S_{14}+t_{15}=147}$

$\implies\mathsf{123+t_{15}=147}$

$\implies\mathsf{t_{15}=147-123}$

$\implies\boxed{\mathsf{t_{15}=24}}$

$\textbf{Find more:}$

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Answer 2

SOLUTION

TO DETERMINE

If for an A.P$\sf{S_{15} = 147 \: \: and \: \: S_{14} =123 \: \: \: then \: \: t_{15} = } \:$

EVALUATION

Let for the given AP

$\sf{n th \: term = \: t_n \: and \: Sum \: of \: first \: n \: terms = S_n}$

Therefore

$\sf{ S_{15} = t_1 + t_2 + t_3 + .... + t_{14} + t_{15}} \: \: - - (1)$

$\sf{ S_{14} = t_1 + t_2 + t_3 + .... + t_{14} } \: \: - - (2)$

Equation 1 - Equation 2 gives

$\sf{S_{15} - S_{14} = t_{15} } \:$

$\sf{ \implies \: t_{15} = S_{15} - S_{14} } \:$

$\sf{ \implies \: t_{15} = 147 - 123 } \:$

$\sf{ \implies \: t_{15} = 24 } \:$

FINAL ANSWER

$\boxed{\sf{ \: \: t_{15} = 24 } \: \:}$

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